ICSE

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions)

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 11 Algebraic Expressions (Including Operations on Algebraic Expressions)

Algebraic Expressions Exercise 11A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Separate the constants and variables from the following :

Solution:

Question 2.
Write the number of terms in each of the following polynomials.
(i) 5x² + 3 x ax
(ii) ax ÷ 4 – 7
(iii) ax – by + y x z
(iv) 23 + a x b ÷ 2.
Solution:

Question 3.
Separate monomials, binomials, trinomials and polynomials from the following algebraic expressions :

Solution:

Question 4.
Write the degree of each polynomial given below :

Solution:

Question 5.
Write the coefficient of :
(i) ab in 7abx ,
(ii) 7a in 7abx ;
(iii) 5x² in 5x² – 5x ;
(iv) 8 in a² – 8ax + a ;
(v) 4xy in x² – 4xy + y².
Solution:

Question 6.
In \(\frac { 5 }{ 7 }\) xy²z³, write the coefficient of

Solution:

Question 7.
In each polynomial, given below, separate the like terms :

Solution:

Algebraic Expressions Exercise 11B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Evaluate :

Solution:

Question 2.
Add :

Solution:

Question 3.
Find the total savings of a boy who saves ₹ (4x – 6y) ; ₹ (6x + 2y) ; ₹ (4y – x) and ₹ (y – 2x) for four consecutive weeks.
Solution:

Question 4.
Subtract :

Solution:

Question 5.
(i) Take away – 3x³ + 4x² – 5x + 6 from 3x³ – 4x² + 5x – 6
(ii) Take m² + m + 4 from -m² + 3m + 6 and the result from m² + m + 1.
Solution:

Question 6.
Subtract the sum of 5y² + y – 3 and y² – 3y + 7 from 6y² + y – 2.
Solution:

Question 7.
What must be added to x⁴ – x³ + x² + x + 3 to obtain x⁴ + x² – 1 ?
Solution:

Question 8.
(i) How much more than 2x² + 4xy + 2y² is 5x² + 10xy – y² ?
(ii) How much less 2a² + 1 is than 3a² – 6 ?
Solution:

Question 9.
If x = 6a + 86 + 9c ; y = 2b – 3a – 6c and z = c – b + 3a ; find
(i) x + y + z
(ii) x – y + z
(iii) 2x – y – 3z
(iv) 3y – 2z – 5x
Solution:

Question 10.
The sides of a triangle are x² – 3xy + 8, 4x² + 5xy – 3 and 6 – 3x² + 4xy. Find its perimeter.
Solution:

Question 11.
The perimeter of a triangle is 8y² – 9y + 4 and its two sides are 3y² – 5y and 4y² + 12. Find its third side.
Solution:

Question 12.
The two adjacent sides of a rectangle are 2x² – 5xy + 3z² and 4xy – x² – z². Find its perimeter.
Solution:

Question 13.
What must be subtracted from 19x⁴ + 2x³ + 30x – 37 to get 8x⁴ + 22x³ – 7x – 60 ?
Solution:

Question 14.
How much smaller is 15x – 18y + 19z than 22x – 20y – 13z + 26 ?
Solution:

Question 15.
How much bigger is 15x²y² – 18xy² – 10x²y than -5x² + 6x²y – 7xy ?
Solution:

Algebraic Expressions Exercise 11C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Multiply :

Solution:

Question 2.
Multiply :

Solution:

Question 3.
Simplify :
(i) (7x – 8) (3x + 2)
(ii) (px – q) (px + q)
(iii) (5a + 5b – c) (2b – 3c)
(iv) (4x – 5y) (5x – 4y)
(v) (3y + 4z) (3y – 4z) + (2y + 7z) (y + z)
Solution:

Question 4.
The adjacent sides of a rectangle are x² – 4xy + 7y² and x³ – 5xy². Find its area.
Solution:

Question 5.
The base and the altitude of a triangle are (3x – 4y) and (6x + 5y) respectively. Find its area.
Solution:

Question 6.
Multiply -4xy³ and 6x²y and verify your result for x = 2 and y= 1.
Solution:

Question 7.
Find the value of (3x³) x (-5xy²) x (2x²yz³) for x = 1, y = 2 and z = 3.
Solution:

Question 8.
Evaluate (3x⁴y²) (2x²y³) for x = 1 and y = 2.
Solution:

Question 9.
Evaluate (x⁵) × (3x²) × (-2x) for x = 1.
Solution:

Question 10.
If x = 2 and y = 1; find the value of (-4x²y³) × (-5x²y⁵).
Solution:

Question 11.
Evaluate:
(i) (3x – 2)(x + 5) for x = 2.
(ii) (2x – 5y)(2x + 3y) for x = 2 and y = 3.
(iii) xz (x² + y²) for x = 2, y = 1 and z= 1.
Solution:

Question 12.
Evaluate:
(i) x(x – 5) + 2 for x = 1.
(ii) xy²(x – 5y) + 1 for x = 2 and y = 1.
(iii) 2x(3x – 5) – 5(x – 2) – 18 for x = 2.
Solution:

Question 13.
Multiply and then verify :
-3x²y² and (x – 2y) for x = 1 and y = 2.
Solution:

Question 14.
Multiply:
(i) 2x² – 4x + 5 by x² + 3x – 7
(ii) (ab – 1)(3 – 2ab)
Solution:

Question 15.
Simplify : (5 – x)(6 – 5x)(2 -x).
Solution:

Algebraic Expressions Exercise 11D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Divide :

Solution:

Question 2.
Find the quotient and the remainder (if any) when :

Solution:

Question 3.
The area of a rectangle is x³ – 8x² + 7 and one of its sides is x – 1. Find the length of the adjacent side.
Solution:
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Question 4.
The product of two numbers is 16x⁴ – 1. If one number is 2x – 1, find the other.
Solution:

Question 5.
Divide x⁶ – y⁶ by the product of x² + xy + y² and x – y.
Solution:

Algebraic Expressions Exercise 11E – Selina Concise Mathematics Class 8 ICSE Solutions

Simplify :
Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 10 Direct and Inverse Variations

Direct and Inverse Variations Exercise 10A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
In which of the following tables, x and y vary directly:

Solution:


Question 2.
If x and y vary directly, find the values of x, y and z:

Solution:

Question 3.
A truck consumes 28 litres of diesel for moving through a distance of 448 km. How much distance will it cover in 64 litres of diesel?
Solution:

Question 4.
For 100 km, a taxi charges ₹ 1,800. How much will it charge for a journey of 120 km?
Solution:

Question 5.
If 27 identical articles cost ₹ 1,890, how many articles can be bought for ₹ 1,750?
Solution:

Question 6.
7 kg of rice costs ₹ 1,120. How much rice can be bought for ₹ 3,680?
Solution:

Question 7.
6 note-books cost ₹ 156, find the cost of 54 such note-books.
Solution:

Question 8.
22 men can dig a 27 m long trench in one day. How many men should be employed for digging 135 m long trench of the same type in one day?
Solution:

Question 9.
If the total weight of 11 identical articles is 77 kg, how many articles of the same type would weigh 224 kg?
Solution:

Question 10.
A train is moving with uniform speed of 120 km per hour.
(i) How far will it travel in 36 minutes?
(ii) In how much time will it cover 210 km?
Solution:

Direct and Inverse Variations Exercise 10B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Check whether x and y vary inversely or not.

Solution:

Question 2.
If x and y vary inversely, find the values of l, m and n :

Solution:

Question 3.
36 men can do a piece of work in 7 days. How many men will do the same work in 42 days?
Solution:

Question 4.
12 pipes, all of the same size, fill a tank in 42 minutes. How long will it take to fill the same tank, if 21 pipes of the same size are used?
Solution:

Question 5.
In a fort 150 men had provisions for 45 days. After 10 days, 25 men left the fort. How long would the food last at the same rate?
Solution:

Question 6.
72 men do a piece of work in 25 days. In how many days will 30 men do the same work?
Solution:

Question 7.
If 56 workers can build a wall in 180 hours, how many workers will be required to do the same work in 70 hours?
Solution:

Question 8.
A car takes 6 hours to reach a destination by travelling at the speed of 50 km per hour. How long will it take when the car travels at the speed of 75 km per hour?
Solution:

Direct and Inverse Variations Exercise 10C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Cost of 24 identical articles is Rs. 108, Find the cost of 40 similar articles.
Solution:

Question 2.
If 15 men can complete a piece of work in 30 days, in how many days will 18 men complete it?
Solution:

Question 3.
In order to complete a work in 28 days, 60 men are required. How many men will be required if the same work is to be completed in 40 days?
Solution:

Question 4.
A fort had provisions for 450 soldiers for 40 days. After 10 days, 90 more soldiers come to the fort. Find in how many days will the remaining provisions last at the same rate?
Solution:

Question 5.
A garrison has sufficient provisions for 480 men for 12 days. If the number of men is reduced by 160; find how long will the provisions last.
Solution:

Question 6.
\(\frac { 3 }{ 5 }\) quintal of wheat costs Rs.210. Find the cost of :
(i) 1 quintal of wheat
(ii) 0.4 quintal of wheat
Solution:

Question 7.
If \(\frac { 2 }{ 9 }\) of a property costs Rs.2,52,000; find the cost of \(\frac { 4 }{ 7 }\) of it.
Solution:

Question 8.
4 men or 6 women earn Rs. 360 in one day. Find, how much will:
(i) a man earn in one day?
(ii) a woman earn in one day?
(iii) 6 men and 4 women earn in one day?
Solution:

Question 9.
16 boys went to the canteen to have tea and snacks together. The bill amounted to Rs. 114.40. What will be the contribution of a boy who pays for himself and 5 others?
Solution:

Question 10.
50 labourers can dig a pond in 16 days. How many labourers will be required to dig another pond, double in size in 20 days?
Solution:

Question 11.
If 12 men or 18 women can complete a piece of work in 7 days, in how many days can 4 men and 8 women complete the same work?
Solution:

Question 12.
If 3 men or 6 boys can finish a work in 20 days, how long will 4 men and 12 boys take to finish the same work ?
Solution:

Question 13.
A particular work can be completed by 6 men and 6 women in 24 days; whereas the same work can be completed by 8 men and 12 women in 15 days. Find :
(i) according to the amount of work done, one man is equivalent to how many women.
(ii) the time taken by 4 men and 6 women to complete the same work.
Solution:

Question 14.
If 12 men and 16 boys can do a piece of work in 5 days and, 13 men and 24 boys can do it in 4 days, how long will 7 men and 10 boys take to do it?
Solution:

Direct and Inverse Variations Exercise 10D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Eight oranges can be bought for Rs. 10.40. How many more can be bought for Rs. 16.90?
Solution:

Question 2.
Fifteen men can build a wall in 60 days. How many more men are required to build another wall of same size in 45 days?
Solution:

Question 3.
Six taps can fill an empty cistern in 8 hours. How much more time will be taken, if two taps go out of order? Assume, all the taps supply water at the same rate.
Solution:

Question 4.
A contractor undertakes to dig a canal, 6 kilometres long, in 35 days and employed 90 men. He finds that after 20 days only 2 km of canal have been completed. How many more men must be employed to finish the work in time?
Solution:

Question 5.
If 10 horses consume 18 bushels in 36 days. How long will 24 bushels last for 30 horses?
Solution:

Question 6.
A family of 5 persons can be main¬tained for 20 days with Rs.2,480. Find, how long Rs.6944 maintain a family of 8 persons
Solution:

Question 7.
90 men can complete a work in 24 days working 8 hours a day. How many men are required to complete the same work in 18 days working 7\(\frac { 1 }{ 2 }\) hours a day?
Solution:

Question 8.
Twelve typists, all working with same speed, type a certain number of pages in 18 days working 8 hours a day. Find, how many hours per day must sixteen typists work in order to type the same number of pages in 9 days?
Solution:

Question 9.
If 25 horses consume 18 quintal in 36 days, how long will 28 quintal last for 30 horses?
Solution:

Question 10.
If 70 men dig 15,000 sq. m of a field in 5 days, how many men will dig 22,500 sq. m field in 25 days?
Solution:

Question 11.
A contractor undertakes to build a wall 1000 m long in 50 days. He employs 56 men, but at the end of 27 days, he finds that only 448 m of wall is built. How many extra men must the contractor employ so that the wall is completed in time ?
Solution:

Question 12.
A group of labourers promises to do a piece of work in 10 days, but five of them become absent. If the remaining labourers complete the work in 12 days, find their original number in the group.
Solution:

Question 13.
Ten men, working for 6 days of 10 hours each, finish \(\frac { 5 }{ 21 }\) of a piece of work. How many men working at the same rate and for the same number of hours each day, will be required to complete the remaining work in 8 days?
Solution:

Direct and Inverse Variations Exercise 10E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A can do a piece of work in 10 days and B in 15 days. How long will they take together to finish it ?
Solution:

Question 2.
A and B together can do a piece of work in 6\(\frac { 2 }{ 3 }\) days ; but B alone can do it in 10 days. How long will A take to do it alone?
Solution:

Question 3.
A can do a work in 15 days and B in 20 days. If they together work on it for 4 days ; what fraction of the work will be left ?
Solution:

Question 4.
A, B and C can do a piece of work in 6 days, 12 days and 24 days respectively. In what time will they all together do it?
Solution:

Question 5.
A and B working together can mow a field in 56 days and with the help of C, they could have mowed it in 42 days. How long would C take by himself?
Solution:

Question 6.
A can do a piece of work in 24 days, A and B can do it in 16 days and A, B and C in 10\(\frac { 2 }{ 3 }\) days. In how many days can A and C do it?
Solution:

Question 7.
A can do a piece of work in 20 days and B in 15 days. They worked together on it for 6 days and then A left. How long will B take to finish the remaining work?
Solution:

Question 8.
A can finish a piece of work in 15 days and B can do it in 10 days. They worked together for 2 days and then B goes away. In how many days will A finish the remaining work?
Solution:

Question 9.
A can do a piece of work in 10 days ; B in 18 days; and A, B and C together in 4 days. In what time would C alone do it ?
Solution:

Question 10.
A can do \(\frac { 1 }{ 4 }\) of a work in 5 days and B can do \(\frac { 1 }{ 3 }\) of the same work in 10 days. Find the number of days in which both working together will complete the work.
Solution:

Question 11.
One tap can fill a cistern in 3 hours and the waste pipe can empty the full cistern in 5 hours. In what time will the empty cistern be full, if the tap and the waste pipe are kept open together?
Solution:

Question 12.
A and B can do a work in 8 days; B and C in 12 days, and A and C in 16 days. In what time could they do it, all working together?
Solution:

Question 13.
A and B complete a piece of work in 24 days. B and C do the same work in 36 days ; and A, B and C together finish it in 18 days. In how many days will (i) A alone,
(ii) C alone,
(iii) A and C together, complete the work?
Solution:

Question 14.
A and B can do a piece of work in 40 days; B and C in 30 days; and C and A in 24 days.
(i) How long will it take them to do the work together?
(ii) In what time can each finish it working alone?
Solution:

Question 15.
A can do a piece of work in 10 days, B in 12 days and C in 15 days. All begin together but A leaves the work after 2 days and B leaves 3 days before the work is finished. How long did the work last?
Solution:

Question 16.
Two pipes P and Q would fill an empty cistern in 24 minutes and 32 minutes respectively. Both the pipes being opened together, find when the first pipe must be turned off so that the empty cistern may be just filled in 16 minutes.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 9 Simple and Compound Interest

Simple and Compound Interest Exercise 9A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the interest and the amount on:
(i) ₹ 750 in 3 years 4 months at 10% per annum.
(ii) ₹ 5,000 at 8% per year from 23rd December 2011 to 29th July 2012.
(iii) ₹ 2,600 in 2 years 3 months at 1% per month.
(iv) ₹ 4,000 in 1\(\frac { 1 }{ 3 }\) years at 2 paise per rupee per month.
Solution:

Question 2.
Rohit borrowed Rs. 24,000 at 7.5 percent per year. How much money will he pay at the end of 4th years to clear his debt?
Solution:

Question 3.
The interest on a certain sum of money is Rs. 1,480 in 2 years and at 10 percent per year. Find the sum of money.
Solution:

Question 4.
On what principal will the simple interest be Rs. 7,008 in 6 years 3 months at 5% per year?
Solution:

Question 5.
Find the principal which will amount to Rs. 4,000 in 4 years at 6.25% Per annum.
Solution:

Question 6.
(i) At what rate per cent per annum will Rs. 630 produce an interest of Rs. 126 in 4 years ?
(ii) At what rate per cent per year will a sum double itself in 6\(\frac { 1 }{ 4 }\) years ?
Solution:

Question 7.
(i) In how many years will Rs.950 produce Rs.399 as simple interest at 7%?
(ii) Find the time in which Rs.1200 will amount to Rs.1536 at 3.5% per year.
Solution:

Question 8.
The simple interest on a certain sum of money is \(\frac { 3 }{ 8 }\) of the sum in 6\(\frac { 1 }{ 4 }\) years. Find the rate percent charged.
Solution:

Question 9.
What sum of money borrowed on 24th May will amount to Rs. 10210.20 on 17th October of the same year at 5 percent per annum simple interest.
Solution:

Question 10.
In what time will the interest on a certain sum of money at 6% be \(\frac { 5 }{ 8 }\) of itself?
Solution:

Question 11.
Ashok lent out Rs.7000 at 6% and Rs.9500 at 5%. Find his total income from the interest in 3 years.
Solution:

Question 12.
Raj borrows Rs.8,000; out of which Rs. 4500 at 5% and the remainder at 6%. Find the total interest paid by him in 4 years.
Solution:

Question 13.
Mohan lends Rs.4800 to John for 4\(\frac { 1 }{ 2 }\) years and Rs.2500 to Shy am for 6 years and receives a total sum of Rs.2196 as interest. Find the rate percent per annum, it being the same in both the cases.
Solution:

Question 14.
John lent Rs. 2550 to Mohan at 7.5 percent per annum. If Mohan discharges the debt after 8 months by giving an old black and white television and Rs. 1422.50; find the price of the television.
Solution:

Simple and Compound Interest Exercise 9B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
The interest on a certain sum of money is 0.24 times of itself in 3 years. Find the rate of interest.
Solution:

Question 2.
If ₹ 3,750 amount to ₹ 4,620 in 3 years at simple interest. Find:
(i) the rate of interest
(ii) the amount of Rs. 7,500 in 5\(\frac { 1 }{ 2 }\) years at the same rate of interest
Solution:

Question 3.
A sum of money, lent out at simple interest, doubles itself in 8 years. Find :
(i) the rate of interest
(ii) in how many years will the sum become triple (three times) of itself at the same rate percent?
Solution:

Question 4.
Rupees 4000 amount to Rs.5000 in 8 years ; in what time will Rs.2100 amount to Rs.2800 at the same rate ?
Solution:

Question 5.
What sum of money lent at 6.5% per annum will produce the same interest in 4 years as Rs.7500 produce in 6 years at 5% per annum?
Solution:

Question 6.
A certain sum amounts to Rs.3825 in 4 years and to Rs.4050 in 6 years. Find the rate percent and the sum.
Solution:

Question 7.
At what rate percent of simple interest will the interest on Rs.3750 be one-fifth of itself in 4 years? To what will it amount in 15 years?
Solution:

Question 8.
On what date will ₹ 1950 lent on 5th January 2011 amount to ₹ 2125.50 at 5 percent per annum simple interest?
Solution:

Question 9.
If the interest on Rs.2400 is more than the interest on Rs.2000 by Rs.60 in 3 years at the same rate percent; find the rate.
Solution:

Question 10.
Divide Rs. 15,600 into two parts such that the interest on one at 5 percent for 5 years may be equal to that on the other at 4\(\frac { 1 }{ 2 }\) per cent for 6 years.
Solution:

Simple and Compound Interest Exercise 9C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A sum of Rs. 8,000 is invested for 2 years at 10% per annum compound interest. Calculate:
(i) interest for the first year.
(ii) principal for the second year.
(iii) interest for the second year.
(iv) final amount at the end of second year
(v) compound interest earned in 2 years.
Solution:

Question 2.
A man borrowed Rs. 20,000 for 2 years at 8% per year compound interest. Calculate :
(i) the interest of the first year.
(ii) the interest of the second year.
(iii) the final amount at the end of second year.
(iv) the compound interest of two years.
Solution:

Question 3.
Calculate the amount and the compound interest on Rs. 12,000 in 2 years and at 10% per year.
Solution:

Question 4.
Calculate the amount and the compound interest on Rs. 10,000 in 3 years at 8% per annum.
Solution:

Question 5.
Calculate the compound interest on Rs. 5,000 in 2 years; if the rates of interest for successive years be 10% and 12% respectively.
Solution:

Question 6.
Calculate the compound interest on Rs. 15,000 in 3 years; if the rates of interest for successive years be 6%, 8% and 10% respectively.
Solution:

Question 7.
Mohan borrowed Rs. 16,000 for 3 years at 5% per annum compound interest. Calculate the amount that Mohan will pay at the end of 3 years.
Solution:

Question 8.
Rekha borrowed Rs. 40,000 for 3 years at 10% per annum compound interest. Calculate the interest paid by her for the second year.
Solution:

Question 9.
Calculate the compound interest for the second year on Rs. 15000 invested for 5 years at 6% per annum.
Solution:

Question 10.
A man invests Rs. 9600 at 10% per annum compound interest for 3 years. Calculate :
(i) the interest for the first year.
(ii) the amount at the end of the first year.
(iii) the interest for the second year.
(iv) the interest for the third year.
Solution:

Question 11.
A person invests Rs. 5,000 for two years at a certain rate of interest compounded annually. At the end of one year, this sum amounts to Rs. 5,600. Calculate :
(i) the rate of interest per year.
(ii) the amount at the end of the second year.
Solution:

Question 12.
Calculate the difference between the compound interest and the simple interest on ₹ 7,500 in two years and at 8% per annum.
Solution:

Question 13.
Calculate the difference between the compound interest and the simple interest on ₹ 8,000 in three years and at 10% per annum.
Solution:

Question 14.
Rohit borrowed ₹ 40,000 for 2 years at 10% per annum C.I. and Manish borrowed the same sum for the same time at 10.5% per annum simple interest. Which of these two gets less interest and by how much?
Solution:

Question 15.
Mr. Sharma borrowed ₹ 24,000 at 13% p.a. simple interest and an equal sum at 12% p.a. compound interest. Find the total interest earned by Mr. Sharma in 2 years.
Solution:

Question 16.
Peter borrows ₹ 12,000 for 2 years at 10% p.a. compound interest. He repays ₹ 8,000 at the end of first year. Find:
(i) the amount at the end of first year, before making the repayment.
(ii) the amount at the end of first year, after making the repayment.
(iii) the principal for the second year.
(iv) the amount to be paid at the end of second year, to clear the account.
Solution:

Question 17.
Gautam takes a loan of ₹ 16,000 for 2 years at 15% p.a. compound interest. He repays ₹ 9,000 at the end of first year. How mucH must he pay at the end of second year to clear the debt?
Solution:

Question 18.
A certain sum of money, invested for 5 years at 8% p.a. simple interest earns an interest of ₹ 12,000. Find:
(i) the sum of money.
(ii) the compound interest earned by this money in two years and at 10% p.a. compound interest.
Solution:

Question 19.
Find the amount and the C.I. on ₹ 12,000 at 10% per annum compounded half-yearly.
Solution:

Question 20.
Find the amount and the C.I. on ₹ 8,000 in 1\(\frac { 1 }{ 2 }\) years at 20% per year compounded half- yearly.
Solution:

Question 21.
Find the amount and the compound interest on ₹ 24,000 for 2 years at 10% per annum compounded yearly.
Solution:

Question 22.
Find the amount and the compound interest on ₹ 16,000 for 3 years at 5% per annum compounded annually.
Solution:

Question 23.
Find the amount and the compound interest on ₹ 20,000 for 1\(\frac { 1 }{ 2 }\) years at 10% per annum compounded half-yearly.
Solution:

Question 24.
Find the amount and the compound interest on ₹ 32,000 for 1 year at 20% per annum compounded half-yearly.
Solution:

Question 25.
Find the amount and the compound interest on ₹ 4,000 in 2 years, if the rate of interest for first year is 10% and for the second year is 15%.
Solution:

Question 26.
Find the amount and the compound interest on ₹ 10,000 in 3 years, if the rates of interest for the successive years are 10%, 15% and 20% respectively.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 8 ICSE Solutions Chapter 8 Profit, Loss and Discount

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 8 Profit, Loss and Discount

Profit, Loss and Discount Exercise 8A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Megha bought 10 note-books for Rs.40 and sold them at Rs.4.75 per note-book. Find, her gain percent.
Solution:

Question 2.
A fruit-seller buys oranges at 4 for Rs.3 and sells them at 3 for Rs.4 Find his profit percent.
Solution:

Question 3.
A man buys a certain number of articles at 15 for Rs. 112.50 and sells them at 12 for Rs.108. Find ;
(i) his gain as percent;
(ii) the number of articles sold to make a profit of Rs.75.
Solution:

Question 4.
A boy buys an old bicycle for Rs. 162 and spends Rs. 18 on its repairs before selling the bicycles for Rs. 207. Find his gain or loss percent.
Solution:

Question 5.
An article is bought from Jaipur for Rs. 4,800 and is sold in Delhi for Rs. 5,820. If Rs. 1,200 is spent on its transportations, etc. ; find he loss or the gain as percent.
Solution:

Question 6.
Mohit sold a T.V. for Rs. 3,600 ; gaining one-sixth of its selling price. Find :
(i) the gain
(ii) the cost price of the T.V.
(iii) the gain percent.
Solution:

Question 7.
By selling a certain number of goods for Rs. 5,500; a shopkeeper loses equal to one-tenth of their selling price. Find :
(i) the loss incured
(ii) the cost price of the goods
(iii) the loss as percent.
Solution:

Question 8.
The selling price of a sofa-set is \(\frac { 4 }{ 5 }\) times of its cost price. Find the gain or the loss as percent.
Solution:

Question 9.
The cost price of an article is \(\frac { 4 }{ 5 }\) times of its selling price. Find the loss or the gain as percent.
Solution:

Question 10.
A shopkeeper sells his goods at 80% of their cost price. Find the percent gain or loses?
Solution:

Question 11.
The cost price of an article is 90% of its selling price. What is the profit or the loss as percent?
Solution:

Question 12.
The cost price of an article is 30 percent less than its selling price. Find, the profit or loss as percent.
Solution:

Question 13.
A shop-keeper bought 300 eggs at 80 paisa each. 30 eggs were broken in transaction and then he sold the remaining eggs at one rupee each. Find, his gain or loss as percent.
Solution:

Question 14.
A man sold his bicycle for Rs.405 losing one-tenth of its cost price, find :
(i) its cc price;
(ii) the loss percent.
Solution:

Question 15.
A man sold a radio-set for Rs.250 and gained one-ninth of its cost price. Find ;
(i) its cost price;
(ii) the profit percent.
Solution:

Profit, Loss and Discount Exercise 8B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the selling price, if:
(i) C.P. = Rs. 950 and profit = 8%
(ii) C.P. = Rs. 1,300 and loss = 13%
Solution:

Question 2.
Find the cost price, if :
(i) S.P. = Rs. 1,680 and profit = 12%
(ii) S.P. = Rs. 1,128 and loss = 6%
Solution:

Question 3.
By selling an article for Rs.900; a man gains 20%. Find his cost price and the gain.
Solution:

Question 4.
By selling an article for Rs.704; a person loses 12%. Find his cost price and the loss
Solution:

Question 5.
Find the selling price, if :
(i) C.P. = Rs.352; overheads = Rs.28 and profit = 20
(ii) C.P. = Rs.576; overheads = Rs.44 and loss = 16%
Solution:

Question 6.
If John sells his bicycle for Rs. 637, he will suffer a loss of 9%. For how much should it be sold, if he desires a profit of 5%?
Solution:

Question 7.
A man sells a radio-set for Rs.605 and gains 10%. At what price should he sell another radio of the same kind, in order to gain 16%?
Solution:

Question 8.
By selling a sofa-set for Rs.2,500; the shopkeeper loses 20%. Find his loss percent or profit percent ; if he sells the same sofa-set for Rs.3150.
Solution:

Question 9.
Mr. Sinha sold two tape-recorders for Rs.990 each; gaining 10% on one and losing 10% on the other. Find his total loss or gain as percent on the whole transaction.
Solution:

Question 10.
A tape-recorder is sold for Rs. 2,760 at a gain of 15% and a C.D. player is sold for Rs. 3,240 at a loss of 10% Find :
(i) the C.P. of the tape-recorder
(ii) the C.P. of the C.D. player.
(iii) the total C.P. of both.
(iv) the total S.P. of both
(v) the gain % or the loss % on the whole
Solution:

Question 11.
Rajesh sold his scooter to Rahim at 8% loss and Rahim, in turn, sold the same scooter to Prem at 5% gain. If Prem paid Rs. 14,490 for the scooter ; find :
(i) the S.P. and the C.P. of the scooter for Rahim
(ii) the S.P. and the C.P. of the scooter for Rajesh
Solution:

Question 12.
John sold an article to Peter at 20% profit and Peter sold it to Mohan at 5% loss. If Mohan paid Rs.912 for the article; find how much did John pay for it ?
Solution:

Profit, Loss and Discount Exercise 8C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
A stationer buys pens at 5 for Rs.28 and sells them at a profit of 25 %. How much should a customer pay; if he buys
(i) only one pen ;
(ii) three pens ?
Solution:

Question 2.
A fruit-seller sells 4 oranges for Rs. 3, gaining 50%. Find :
(i) C.P. of 4 oranges,
(ii) C.P. of one orange.
(iii) S.P. of one orange.
(iv) profit made by selling one orange.
(v) number of oranges brought and sold in order to gain Rs. 24.
Solution:

Question 3.
A man sells 12 articles for Rs. 80 gaining 33\(\frac { 1 }{ 3 }\) %. Find the number of articles bought by the man for Rs. 90.
Solution:

Question 4.
The cost price of 20 articles is same as the selling price of 16 articles. Find the gain percent.
Solution:

Question 5.
The selling price of 15 articles is equal to the cost price of 12 articles. Find the gain or loss as percent.
Solution:

Question 6.
By selling 8 pens, Shyam loses equal to the cost price of 2 pens. Find his loss percent.
Solution:

Question 7.
A shop-keeper bought rice worth Rs.4,500. He sold one-third of it at 10% profit.
If he desires a profit of 12% on the whole ; find :
(i) the selling price of the rest of the rice ;
(ii) the percentage profit on the rest of the rice.
Solution:

Question 8.
Mohan bought a certain number of note-books for Rs.600. He sold \(\frac { 1 }{ 4 }\) of them at 5 percent loss. At what price should he sell the remaining note-books so as to gain 10% on the whole ?
Solution:

Question 9.
Raju sells a watch at 5% profit. Had he sold it for Rs.24 more ; he would have gained 11%. Find the cost price of the watch.
Solution:

Question 10.
A man sold a bicycle at 5% profit. If the cost had been 30% less and the selling price Rs.63 less, he would have made a profit of 30%. What is the cost price of the bicycle?
Solution:

Question 11.
Renu sold an article at a loss of 8 percent. Had she bought it at 10% less and sold for Rs.36 more; she would have gained 20%. Find the cost price of the article.
Solution:

Profit, Loss and Discount Exercise 8D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
An article is marked for Rs. 1,300 and is sold for Rs. 1,144 ; find the discount percent.
Solution:

Question 2.
The marked price of a dinning table is Rs. 23,600 and is available at a discount of 8%. Find its selling price.
Solution:

Question 3.
A wrist-watch is available at a discount of 9%. If the list-price of the watch is Rs. 1,400 ; find the discount given and the selling price of the watch.
Solution:

Question 4.
A shopkeeper sells an article for Rs. 248.50 after allowing a discount of 10%. Find the list price of the article.
Solution:

Question 5.
A shop-keeper buys an article for Rs.450. He marks it at 20% above the cost price. Find :
(i) the marked price of the article.
(ii) the selling price, if he sells the articles at 10 percent discount.
(iii) the percentage discount given by him, if he sells the article for Rs.496.80
Solution:

Question 6.
The list price of an article is Rs.800 and is available at a discount of 15 percent. Find :
(i) selling price of the article ;
(ii) cost price of the article, if a profit of 13\(\frac { 1 }{ 3 }\) % is made on selling it.
Solution:

Question 7.
An article is marked at Rs. 2,250. By selling it at a discount of 12%, the dealer makes a profit of 10%. Find :
(i) the selling price of the article.
(ii) the cost price of the article for the dealer.
Solution:

Question 8.
By selling an article at 20% discount, a shopkeeper gains 25%. If the selling price of the article is Rs. 1,440 ; find :
(i) the marked price of the article.
(ii) the cost price of the article.
Solution:

Question 9.
A shop-keeper marks his goods at 30 percent above the cost price and then gives a discount of 10 percent. Find his gain percent.
Solution:

Question 10.
A ready-made garments shop in Delhi, allows 20 percent discount on its garments and still makes a profit of 20 percent. Find the marked price of a dress which is bought by the shop-keeper for Rs.400.
Solution:

Question 11.
At 12% discount, the selling price of a pen is Rs. 13.20. Find its marked price. Also, find the new selling price of the pen, if it is sold at 5% discount.
Solution:

Question 12.
The cost price of an article is Rs. 2,400 and it is marked at 25% above the cost price. Find the profit and the profit percent, if the article is sold at 15% discount.
Solution:

Question 13.
Thirty articles are bought at Rs. 450 each. If one-third of these articles be sold at 6% loss; at what price must each of the remaining articles be sold in order to make a profit of 10% on the whole?
Solution:

Question 14.
The cost price of an article is 25% below the marked price. If the article is available at 15% discount and its cost price is Rs. 2,400; find:
(i) Its marked price
(ii) its selling price
(iii) the profit percent.
Solution:

Question 15.
Find a single discount (as percent) equivalent to following successive discounts:
(i) 20% and 12%
(ii) 10%, 20% and 20%
(iii) 20%, 10% and 5%
Solution:

Question 16.
Find the single discount (as percent) equivalent to successive discounts of:
(i) 80% and 80%
(ii) 60% and 60%
(iii) 60% and 80%
Solution:

Profit, Loss and Discount Exercise 8E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Rajat purchases a wrist-watch costing Rs. 540. The rate of Sales Tax is 8%. Find the total amount paid by Rajat for the watch.
Solution:

Question 2.
Ramesh paid ₹ 345.60 as Sales Tax on a purchase of ₹ 3,840. Find the rate of Sales Tax.
Solution:

Question 3.
The price of a washing machine, inclusive of sales tax is ₹ 13,530/-. If the Sales Tax is 10%, find its basic (cost) price.
Solution:

Question 4.
Sarita purchases biscuits costing ₹ 158 on which the rate of Sales Tax is 6%. She also purchases some cosmetic goods costing ₹ 354 on which rate of Sales Tax is 9%. Find the total amount to be paid by Sarita.
Solution:

Question 5.
The price of a T.V. set inclusive of sales tax of 9% is ₹ 13,407. Find its marked price. If Sales Tax is increased to 13%, how much more does the customer has to pay for the T.V. ?
Solution:

Question 6.
The price of an article is ₹ 8,250 which includes Sales Tax at 10%. Find how much more or less does a customer pay for the article, if the Sales Tax on the article:
(i) increases to 15%
(ii) decreases to 6%
(iii) increases by 2%
(iv) decreases by 3%
Solution:

Question 7.
A bicycle is available for ₹ 1,664 including Sales Tax. If the list price of the bicycle is ₹ 1,600, find :
(i) the rate of Sales Tax
(ii) the price a customer will pay for the bicycle if the Sales Tax is increased by 6%.
Solution:

Question 8.
When the rate of sale-tax is decreased from 9% to 6% for a coloured T.V. ; Mrs. Geeta will save ₹ 780 in buying this T.V. Find the list price of the T.V.
Solution:

Question 9.
A shopkeeper sells an article for ₹ 21,384 including 10% sales-tax. However, the actual rate of sales-tax is 8%. Find the extra profit made by the dealer.
Solution:

Profit, Loss and Discount Exercise 8F – Selina Concise Mathematics Class 8 ICSE Solutions

[In this exercise, all the prices are excluding tax/VAT unless specified]
Question 1.
A shopkeeper buys an article for ₹ 8,000 and sells it for ₹ 10,000. If the rate of tax under VAT is 10%, find :
(i) tax paid by the shopkeeper
(ii) tax charged by the shopkeeper
(iii) VAT paid by the shopkeeper
Solution:

Question 2.
A trader buys some goods for ₹ 12,000 and sells them for ₹ 15,000. If the rate of tax under VAT is 12%, find the VAT paid by the trader?
Solution:

Question 3.
The marked price of an article is ₹ 7,000 and is available at 20% discount. Manoj buys this article and then sold it at its marked price. If the rate of tax at each state is 10%, find the VAT paid by Manoj.
Solution:

Question 4.
A buys some goods for ₹ 4,000 and sold them to B for ₹ 5,000. B sold these goods to C for ₹ 6,000. If the rate of tax (under VAT) at each stage is 5%, find :
(i) VAT paid by A
(ii) VAT paid by B
Solution:

Question 5.
A buys an article for ₹ 8,000 and sold it to B at 20% profit. If the rate of tax under VAT is 8%, find :
(i) tax paid by A
(ii) tax charged by A
(iii) VAT paid by A
Solution:

Question 6.
A shopkeeper purchases an article for ₹ 12,400 and sells it to a customer for ₹ 17,000. If the tax under VAT is 8%, find the VAT paid by the shopkeeper.
Solution:

Question 7.
A purchases an article for ₹ 7,200 and sells it to B for ₹ 9,600. B, in turn, sells the article to C for ₹ 11,000. If the tax (under VAT) is 10%, find the VAT paid by A and B.
Solution:

Question 8.
A manufacturer buys some goods for ₹ 60,000 and pays 5% tax. He sells these goods for ₹ 80,000 and charges tax at the rate of 12%. Find the VAT paid by the manufacturer.
Solution:

Question 9.
The cost of an article is ₹ 6,000 to a distributor, he sells it to a trader for ₹ 7,500 and the trader sells it further to a customer for ₹ 8,000. If the rate of tax under VAT is 8%; find the VAT paid by the:
(i) distributor
(ii) trader
Solution:

Question 10.
The marked price of an article is ₹ 10,000. A buys it at 30% discount on the marked price and sells it at 10% discount on the marked price. If the rate of tax under VAT is 5%, find the amount of VAT paid by A.
Solution:

Selina Concise Mathematics Class 8 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 22 Probability

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 22 Probability

Probability Exercise 22A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
A coin is tossed once. Find the probability of
(i) getting a head
(ii) not getting a head
Solution:

Question 2.
A coin is tossed 80 times and the head is obtained 38 times. Now, if a coin tossed once, what will the probability of getting:
(i) a tail
(ii) ahead
Solution:

Question 3.
A dice is thrown 20 times and the outcomes are noted as shown below :

Now a dice is thrown at random, find the probability of getting :
Solution:

Question 4.
A survey of 50 boys showed that 21 like tea while 29 dislike it. Out of these boys, one boy is chosen at random. What is the probability that the chosen boy
(i) likes tea
(ii) dislikes tea
Solution:

Question 5.
In a cricket match, a batsman hits a boundary 12 times out of 80 balls he plays, further, if he plays one ball more, what will be the probability that:
(i) he hits a boundary
(ii) he does not hit a boundary
Solution:

Question 6.
There are 8 marbles in a bag with numbers from 1 to 8 marked on each of them. What is the probability of drawing a marble with number
(i) 3
(ii) 7
Solution:

Question 7.
Two coins are tossed simultaneously 100 times and the outcomes are as given below:

If the same pair of coins is tossed again at random, find the probability of getting :
(i) two heads
(ii) exactly one head
(iii) no head.
Solution:

Question 8.
A bag contains 4 white and 6 black balls,- all of the same shape and same size. A ball is drawn from the bag without looking into the bag. Find the probability that the ball drawn is :
(i) a black ball
(ii) a white ball
(iii) not a black ball
Solution:

Question 9.
In a single throw of a dice, find the probability of getting a number:
(i) 4
(ii) 6
(iii) greater than 4
Solution:

Question 10.
Hundred identical cards are numbered from 1 to 100. The cards are well shuffled and then a card is drawn. Find the probability that the number on the card drawn is :
(i) 50
(ii) 80
(iii) 40
Solution:

Probability Exercise 22B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Suppose S is the event that will happen tommorow and P(S) = 0.03.
(i) State in words, the complementary event S’.
(ii) Find P(S’)
Solution:

Question 2.
Five Students A, B, C, D and E are competing in a long distance race. Each student’s probability of winning the race is given below:
A → 20 %, B → 22 %, C → 7 %, D → 15% and E → 36 %
(i) Who is most likely to win the race ?
(ii) Who is least likely to win the race ?
(iii) Find the sum of probabilities given.
(iv) Find the probability that either A or D will win the race.
(v) Let S be the event that B will win the race.
(a) Find P(S)
(b) State, in words, the complementary event S’.
(c) Find P(S’)
Solution:

Question 3.
A Ticket is randomly selected from a basket containing3 green, 4 yellow and 5 blue tickets. Determine the probability of getting:
(i) a green ticket
(ii) a green or yellow ticket.
(iii) an orange ticket.
Solution:

Question 4.
Ten cards with numbers 1 to 10 written on them are placed in a bag. A card is chosen from the bag at random. Determine the probability of choosing:
(i) 7
(ii) 9 or 10
(iii) a number greater than 4
(iv) a number less than 6
Solution:

Question 5.
A carton contains eight brown and four white eggs. Find the probability that an egg selected at random is :
(i) brown
(ii) white
Solution:

Question 6.
A box contains 3 yellow, 4 green and 8 blue tickets. A ticket is chosen at random. Find the probability that the ticket is :
(i) yellow
(ii) green
(iii) blue
(iv) red
(v) not yellow
Solution:

Question 7.
The following table shows number of males and number of females of a small locality in different age groups.
If one of the persons, from this locality, is picked at random, what is the probability that
(a) the person picked is a male ?
(b) the person picked is a female ?
(c) the person picked is a female aged 21-50 ?
(d) the person is a male with age upto 50 years?

Solution:

Selina Concise Mathematics Class 7 ICSE Solutions