ICSE

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 6 Ratio and Proportion (Including Sharing in a Ratio)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 6 Ratio and Proportion (Including Sharing in a Ratio)

Ratio and Proportion Exercise 6A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Express each of the given ratio in its simplest form :

Solution:

Question 2.
Divide 64 cm long string into two parts in the ratio 5 : 3.
Solution:

Question 3.
Rs. 720 is divided between x and y in the ratio 4:5. How many rupees will each get?
Solution:

Question 4.
The angles of a triangle are in the ratio 3 :2 : 7. Find each angle.
Solution:

Question 5.
A rectangular field is 100 m by 80 m. Find the ratio of
(i) length to its breadth
(ii) breadth to its perimeter.
Solution:

Question 6.
The sum of three numbers, whose ratios are 3 \(\frac { 1 }{ 3 }\) : 4 \(\frac { 1 }{ 5 }\) : 6 \(\frac { 1 }{ 8 }\) is 4917.Find the numbers.
Solution:

Question 7.
The ratio between two quantities is 3 : the first is Rs. 810, find the second.
Solution:

Question 8.
Two numbers are in the ratio 5 : 7. Their difference is 10. Find the numbers.
Solution:

Question 9.
Two numbers are in the ratio 10 : 11. Their sum is 168. Find the numbers.
Solution:

Question 10.
A line is divided in two parts in the ratio 2.5 : 1.3. If the smaller one is 35.1 cm, find the length of the line.
Solution:

Question 11.
In a class, the ratio of boys to the girls is 7:8. What part of the whole class are girls.
Solution:

Question 12.
The population of a town is ’ 50,000, out of which males are \(\frac { 1 }{ 3 }\) of the whole population. Find the number of females. Also, find the ratio of the number of females to the whole population.
Solution:

Question 13.
Ten gram of an alloy of metals A and B contains 7.5 gm of metal A and the rest is metal B. Find the ratio between :
(i) the weights of metals A and B in the alloy.
(ii) the weight of metal B and the weight of the alloy.
Solution:

Question 14.
The ages of two boys A and B are 6 years 8 months and 7 years 4 months respectively. Divide Rs. 3,150 in the ratio of their ages.
Solution:

Question 15.
Three persons start a business and spend Rs. 25,000; Rs. 15,000 atid Rs. 40,000 respectively. Find the share of each out of a profit of Rs. 14,400 in a year.
Solution:

Question 16.
A plot of land, 600 sq m in area, is divided between two persons such that the first person gets three-fifth of what the second gets. Find the share of each.
Solution:

Question 17.
Two poles of different heights are standing vertically on a horizontal field. At a particular time, the ratio between the lengths of their shadows is 2 :3. If the height of the smaller pole is 7.5 m, find the height of the other pole.
Solution:

Question 18.
Two numbers are in the ratio 4 : 7. If their L.C.M. is 168, find the numbers.
Solution:

Question 19.
is divided between A and B in such a way that A gets half of B. Find :
(i) the ratio between the shares of A and B.
(ii) the share of A and the share of B.
Solution:

Question 20.
The ratio between two numbers is 5 : 9. Find the numbers, if their H.C.F. is 16.
Solution:

Question 21.
A bag contains ₹ 1,600 in the form of ₹10 and ₹20 notes. If the ratio between the numbers of ₹10 and ₹20 notes is 2 : 3; find the total number of notes in all.
Solution:

Question 22.
The ratio between the prices of a scooter and a refrigerator is 4 : 1. If the scooter costs ₹45,000 more than the refrigerator, find the price of the refrigerator.
Solution:

Ratio and Proportion Exercise 6B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Check whether the following quantities form a proportion or not ?

Solution:

Question 2.
Find the fourth proportional of

Solution:

Question 3.
Find the third proportional of

Solution:

Question 4.
Find the mean proportional between

Solution:

Question 5.


Solution:

Question 6.
If x: y – 5 :4 and 2 : x = 3 :8, find the value of y.
Solution:

Question 7.
Find the value of x, when 2.5 : 4 = x : 7.5.
Solution:

Question 8.
Show that 2, 12 and 72 are in continued proportion.
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions (Including Evaluation)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 21 Framing Algebraic Expressions (Including Evaluation)

Framing Algebraic Expressions Exercise 21 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write in the form of an algebraic expression :
(i) Perimeter (P) of a rectangle is two times the sum of its length (l) and its breadth (b).
(ii) Perimeter (P) of a square is four times its side.
(iii) Area of a square is square of its side.
(iv) Surface area of a cube is six times the square of its edge.
Solution:

Question 2.
Express each of the following as an algebraic expression :
(i) The sum of x and y minus m.
(ii) The product of x and y divided by m.
(iii) The subtraction of 5m from 3n and then adding 9p to it.
(iv) The product of 12, x, y and z minus the product of 5, m and n.
(v) Sum of p and 2r – s minus sum of a and 3n + 4x.
Solution:

Question 3.
Construct a formula for the following :
Total wages (₹ W) of a man whose basic wage is (₹ B) for t hours week plus (₹ R) per hour, if he Works a total of T hours.
Solution:

Question 4.
If x = 4, evaluate :
(i) 3x + 8
(ii) x² – 2x
(iii) \(\frac { { x }^{ 2 } }{ 2 }\)
Solution:

Question 5.
If m – 6, evaluate :
(i) 5m – 6
(ii) 2m² + 3m
(iii) (2m)²
Solution:

Question 6.
If x = 4, evaluate :
(i) 12x + 7
(ii) 5x² + 4x
(iii) \(\frac { { x }^{ 2 } }{ 8 }\)
Solution:

Question 7.
If m = 2, evaluate :
(i) 16m – 7
(ii) 15m² – 10m
(iii) \(\frac { 1 }{ 4 } \times { m }^{ 3 }\)
Solution:

Question 8.
If x = 10, evaluate :
(i) 100x + 225
(ii) 6x² – 25x
(iii) \(\frac { 1 }{ 50 } \times { x }^{ 3 }\)
Solution:

Question 9.
If a = – 10, evaluate :
(i) 5a
(ii) a²
(iii) a³
Solution:

Question 10.
If x = – 6, evaluate :
(i) 11x
(ii) 4x²
(iii) 2x³
Solution:

Question 11.
If m = – 7, evaluate :
(i) 12m
(ii) 2m²
(iii) 2m³
Solution:

Question 12.
Find the average (A) of four quantities p, q, r and s. If A = 6, p = 3, q = 5 and r = 7 ; find the value of s.
Solution:

Question 13.
If a = 5 and b = 6, evaluate :
(i) 3ab
(ii) 6a²b
(iii) 2b²
Solution:

Question 14.
If x = 8 and y = 2, evaluate :
(i) 9xy
(ii) 5x²y
(iii) (4y)²
Solution:

Question 15.
If x = 5 and y = 4, evaluate :
(i) 8xy
(ii) 3x²y
(iii) 3y²
Solution:

Question 16.
If y = 5 and z = 2, evaluate :
(i) 100yz
(ii) 9y²z
(iii) 5y²
(iv) (5z)³
Solution:

Question 17.
If x = 2 and y = 10, evaluate :
(i) 30xy
(ii) 50xy²
(iii) (10x)²
(iv) 5y²
Solution:

Question 18.
If m = 3 and n = 7, evaluate :
(i) 12mn
(ii) 5mn²
(iii) (10m)²
(iv) 4n²
Solution:

Question 19.
If a = -10, evaluate :
(i) 3a – 2
(ii) a² + 8a
(iii) \(\frac { 1 }{ 5 }\) x a²
Solution:

Question 20.
If x = -6, evaluate :
(i) 4x – 9
(ii) 3x² + 8x
(iii) \(\frac { { x }^{ 2 } }{ 2 }\)
Solution:

Question 21.
If m = -8, evaluate :
(i) 2m + 21
(ii) m² + 9m
(iii) \(\frac { { m }^{ 2 } }{ 4 }\)
Solution:

Question 22.
If p = -10, evaluate :
(i) 6p + 50
(ii) 3p² – 20p
(iii) \(\frac { { p }^{ 2 } }{ 50 }\)
Solution:

Question 23.
If y = -8, evaluate :
(i) 6y + 53
(ii) y² + 12y
(iii) \(\frac { { y }^{ 3 } }{ 4 }\)
Solution:

Question 24.
If x = 2 and 7 = -4, evaluate :
(i) 11xy
(ii) 5x²y
(iii) (5y)²
(iv) 8x²
Solution:

Question 25.
If m = 9 and n = -2, evaluate
(i) 4mn
(ii) 2m²n
(iii) (2n)³
Solution:

Question 26.
If m = -8 and n = -2, evaluate :
(i) 12mn
(ii) 3m²n
(iii) (4n)²
Solution:

Question 27.
If x = -5 and y = -8, evaluate :
(i) 4xy
(ii) 2xy²
(iii) 4x²
(iv) 3y²
Solution:

Question 28.
Find T, if T = 2a – b, a = 7 and b = 3.
Solution:

Question 29.
From the formula B = 2a² – b², calculate the value of B when a = 3 and b = -1.
Solution:

Question 30.
The wages ₹ W of a man earning ₹ x per hour for t hours are given by the formula W = xt. Find his wages for working 40 hours at a rate of ₹ 39.45 per hour.
Solution:

Question 31.
The temperature in Fahrenheit scale is represented by F and the tempera¬ture in Celsius scale is represented by C. If F = \(\frac { 9 }{ 5 }\) x C + 32, find F when C = 40.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 5 Exponents (Including Laws of Exponents)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 5 Exponents (Including Laws of Exponents)

Exponents Exercise 5A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the value of:
(i) 6²
(ii) 7³
(iii) 4⁴
(iv) 5⁵
(v) 8³
(vi) 7⁵
Solution:

Question 2.
Evaluate:
(i) 2³ x 4²
(ii) 2³ x 5²
(iii) 3³ x 5²
(iv) 2² x 3³
(v) 3² x 5²
(vi) 5³ x 2⁴
(vii) 3² x 4²
(ix) (5 x 4)²
Solution:

Question 3.
Evaluate:

Solution:

Question 4.
Evaluate :

Solution:

Question 5.
Which is greater :
(i) 2³ or 3²
(ii) 2⁵ or 5²
(iii) 4³ or 3⁴
(iv) 5⁴ or 4⁵
Solution:

Question 6.
Express each of the following in exponential form :
(i) 512
(ii) 1250
(iii) 1458
(iv) 3600
(v) 1350
(vi) 1176
Solution:

Question 7.
If a = 2 and b = 3, find the value of:
(i) (a + b)²
(ii) (b – a)³
(iii) (a x b)^a
(iv) (a x b)^b
Solution:

Question 8.
Express:
(i) 1024 as a power of 2.
(ii) 343 as a power of 7.
(iii) 729 as a power of 3.
Solution:

Question 9.
If 27 x 32 = 3^x x 2^y; find the values of x and y.

Solution:

Question 10.
If 64 x 625 = 2^a x 5^b; find :
(i) the values of a and b.
(ii) 2^b x 5^a
Solution:

Exponents Exercise 5B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Fill in the blanks:
In 5² = 25, base = ……… and index = ……….
If index = 3x and base = 2y, the number = ………
Solution:

Question 2.
Evaluate:
(i) 2⁸ ÷ 2³
(ii) 2^3÷ 2⁸
(iii) (2⁶)⁰
(iv) (3^o)⁶
(v) 8³ x 8^-5 x 8⁴
(vi) 5⁴  x 5³ + 5⁵
(vii) 5⁴ ÷ 5³ x 5⁵
(viii) 4⁴ ÷ 4³ x 4⁰
(ix) (3⁵ x 4⁷ x 5⁸)⁰
Solution:

Question 3.
Simplify, giving Solutions with positive index:


Solution:

Question 4.
Simplify and express the Solution in the positive exponent form :


Solution:

Question 5.
Evaluate

Solution:

Question 6.
If m² = -2 and n = 2; find the values of:
(i) m + r² – 2mn
(ii) mⁿ + n^m
(iii) 6m^-3 + 4n²
(iv) 2n³ – 3m
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution (Including Use of Brackets as Grouping Symbols)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 20 Substitution (Including Use of Brackets as Grouping Symbols)

Substitution Exercise 20A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the following blanks, when :
x = 3,y = 6, z = 18, a = 2, b = 8, c = 32 and d = 0.


Solution:

Question 2.
Find the value of :

Solution:

Question 3.
Find the value of :

Solution:

Question 4.
If a = 3, b = 0, c = 2 and d = 1, find the value of :

Solution:

Question 5.
Find the value of 5x² – 3x + 2, when x = 2.
Solution:

Question 6.
Find the value of 3x³ – 4x² + 5x – 6, when x = -1.
Solution:

Question 7.
Show that the value of x³ – 8x² + 12x – 5 is zero, when x = 1.
Solution:

Question 8.
State true and false :
(i) The value of x + 5 = 6, when x = 1
(ii) The value of 2x – 3 = 1, when x = 0
(iii) \(\frac { 2x-4 }{ x+1 }\) = -1,when x = 1
Solution:

Question 9.
If x = 2, y = 5 and z = 4, find the value of each of the following :

Solution:

Question 10.
If a = 3, find the values of a² and 2^a.
Solution:

Question 11.
If m = 2, find the difference between the values of 4m³ and 3m⁴.
Solution:

Substitution Exercise 20B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Evaluate :
(i) (23 – 15) + 4
(ii) 5x + (3x + 7x)
(iii) 6m – (4m – m)
(iv) (9a – 3a) + 4a
(v) 35b – (16b + 9b)
(vi) (3y + 8y) – 5y
Solution:

Question 2.
Simplify :


Solution:

Question 3.
Simplify :

Solution:

Substitution Exercise 20C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :

Solution:

Question 2.
Insert the bracket as indicated :

Solution:

Substitution Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the value of 3ab + 10bc – 2abc when a = 2, b = 5 and c = 8.
Solution:

Question 2.
If x = 2, y = 3 and z = 4, find the value of 3x² – 4y² + 2z².
Solution:

Question 3.
If x = 3, y = 2 and z = 1; find the value of:
(i) x^y
(ii) y^x
(iii) 3x² – 5y²
(iv) 2x – 3y + 4z + 5
(v) y² – x² + 6z²
(vi) xy + y²z – 4zx
Solution:

Question 4.
If P = -12x² – 10xy + 5y², Q = 7x² + 6xy + 2y², and R = 5x² + 2xy + 4y² ; find :
(i) P – Q
(ii) Q + P
(iii) P – Q + R
(iv) P + Q + R
Solution:

Question 5.
If x = a² – bc, y = b² – ca and z = c² – ab ; find the value of :
(i) ax + by + cz
(ii) ay – bx + cz
Solution:

Question 6.
Multiply and then evaluate :
(i) (4x + y) and (x – 2y); when x = 2 and y = 1.
(ii) (x² – y) and (xy – y²); when x = 1 and y = 2.
(iii) (x – 2y + z) and (x – 3z); when x = -2, y = -1 and z = 1.
Solution:

Question 7.
Simplify :
(i) 5 (x + 3y) – 2 (3x – 4y)
(ii) 3x – 8 (5x – 10)
(iii) 6 {3x – 8 (5x – 10)}
(iv) 3x – 6 {3x – 8 (5x – 10)}
(v) 2 (3x² – 4x – 8) – (3 – 5x – 2x²)
(vi) 8x – (3x – \(\bar { 2x-3 }\))
(vii) 12x² – (7x – \(\bar { 3x^{ 2 }+15 }\))
Solution:

Question 8.
If x = -3, find the value of : 2x³ + 8x² – 15.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations (Related to Algebraic Expressions)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 19 Fundamental Operations (Related to Algebraic Expressions)

Fundamental Operations Exercise 19A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) 5 + 4 = ………… and 5x + 4x = ………….
(ii) 12 + 18 = ………… and 12x²y + 18x²y = ………….
(iii) 7 + 16 = ………….. and 7a + 16b = …………
(iv) 1 + 3 = ………… and x²y + 3xy² = ………..
(v) 7 – 4 = …………… and 7ab – 4ab = …………..
(vi) 12 – 5 = ………… and 12x – 5y = ……………
(vii) 35 – 16 = ………….. and 35ab – 16ba = ………….
(viii) 28 – 13 = …………. and 28ax² – 13a²x = ………….
Solution:

Question 2.
Fill in the blanks :
(i) The sum of – 2 and – 5 = …………. and the sum of – 2x and – 5x = …………….
(ii) The sum of 8 and – 3 = ………….. and the sum of 8ab and – 3ab = ………….
(iii) The sum of – 15 and – 4 = …………….. and the sum of – 15x and -4y = ………………
(iv) 15 + 8 + 3 = ……….. and 15x + 8y + 3x = …………….
(v) 12 – 9 + 15 = …………… and 12ab – 9ab + 15ba = ……………..
(vi) 25 – 7 – 9 = and 25xy – 7xy – 9yx = ……………
(vii) – 4 – 6 – 5 = …………. and – 4ax – 6ax – 5ay = …………….
Solution:

Question 3.
Add:
(i) 8xy and 3xy
(ii) 2xyz, xyz and 6xyz
(iii) 2a, 3a and 4b
(iv) 3x and 2y
(v) 5m, 3n and 4p
(vi) 6a, 3a and 9ab
(vii) 3p, 4q and 9q
(viii) 5ab, 4ba and 6b
(ix) 50pq, 30pq and 10pr
(x) – 2y, – y and – 3y
(xi) – 3b and – b
(xii) 5b, – 4b and – 10b
(xiii) – 2c, – c and – 5c
Solution:

Question 4.
Evaluate :

Solution:

Question 5.
Evaluate :

Solution:

Question 6.
Subtract the first term from the second :

Solution:

Question 7.
Simplify :


Solution:

Fundamental Operations Exercise 19B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the sum of :

Solution:

Question 2.
Add the following expressions :


Solution:

Question 3.
Evaluate :

Solution:

Question 4.
Subtract :

Solution:

Question 5.

Solution:

Question 6.
From the sum of x + y – 2z and 2x – y + z subtract x + y + z.
Solution:

Question 7.
From the sum of 3a – 2b + 4c and 3b – 2c subtract a – b – c.
Solution:

Question 8.
Subtract x – 2y – z from the sum of 3x – y + z and x + y – 3z.
Solution:

Question 9.
Subtract the sum of x + y and x – z from the sum of x – 2z and x + y + z
Solution:

Question 10.
By how much should x + 2y – 3z be increased to get 3x ?
Solution:

Question 11.
The sum of two expressions is 5x² – 3y². If one of them is 3x² + 4xy – y², find the other.
Solution:

Question 12.
The sum of two expressions is 3a² + 2ab – b². If one of them is 2a² + 3b², find the other.
Solution:

Fundamental Operations Exercise 19C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :

Solution:

Question 2.
Fill in the blanks :

Solution:

Question 3.
Find the value of :

Solution:

Question 4.
Multiply :


Solution:

Question 5.
Multiply :

Solution:

Question 6.
Multiply :

Solution:

Question 7.
Multiply :
(i) x + 2 and x + 10
(ii) x + 5 and x – 3
(iii) x – 5 and x + 3
(iv) x – 5 and x – 3
(v) 2x+ y and x+ 3y
(vi) (3x – 5y) and (x + 6y)
(vii) (x + 9y) and (x – 5y)
(viii) (2x + 5y) and (2x + 5y)
Solution:

Question 8.
Multiply :

Solution:

Question 9.
Find the product of :

Solution:

Fundamental Operations Exercise 19D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Divide :

Solution:

Question 2.
Simplify :


Solution:

Question 3.
Divide :


Solution:

Question 4.
Simplify :

Solution:

Question 5.
Divide :


Solution:

Selina Concise Mathematics Class 6 ICSE Solutions