ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 9 Direct and Inverse Variation Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) Two quantities are said to be in direct variation if the increase (or decrease) in one quantity causes in ………….. other quantity.
(ii) Two quantities X and Y are said to be in inverse variation if XY is …………..
(iii) The total cost of articles varies ………….. to the number of articles purchased.
(iv) More work is done in ………….. time.
(v) The time taken to finish work varies ………….. to the number of men at work.
(vi) The speed of a moving object varies inversely to the ………….. to cover a certain distance.
(vii) The number of articles varies ………….. with the cost per article if a fixed amount is available.
(viii)Remuneration is in ………….. of work done.
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Two quantities x andy are said to be in inverse variation if \(\frac{x}{y}\) is constant.
(ii) Number of days needed to complete the work = \(\frac{1}{\text { one day’s work }}\)
(iii) Two quantities x andy are said to be in direct variation if x = ky, where k is constant of variation.
(iv) The work done varies inversely to the number of men at work.
(v) In the given time, the distance covered by a moving object varies directly to its speed.
(vi) If A can complete a work in n days, then A’s one day’s work is \(\frac{1}{n}\) of the work, n
(vii) More the money deposited in a bank, more is the interest earned.
(viii) If the number of articles purchased increases the total cost decreases.
(ix) At the same time length of shadow is in direct variation with length of the object.
(x) The distance covered varies inversely to the consumption of petrol.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 13):
Question 3.
Two quantities x and y are said to be in inverse variation if
(a) xy = k
(b) x ∝ \(\frac{1}{y}\)
(c) x = \(\frac{k}{y}\)
(d) all of these
Solution:

Question 4.
If 12-metre wire costs ₹24, then the cost of 8-metre wire is
(a) ₹16
(b) ₹20
(c) ₹12
(d) ₹18
Solution:

Question 5.
If 5 kg wheat cost ₹60, then cost of 20 kg wheat is
(a) ₹200
(b) ₹210
(c) ₹220
(d) ₹240
Solution:

Question 6.
If 10-men can complete a work in 6 days, then 30 men can complete the same work in
(a) 2 days
(b) 3 days
(c) 4 days
(d) 5 days
Solution:

Question 7.
A car travels 80 km in 5 litres of petrol, then the distance covered by it in 15 litres of petrol is
(a) 400 km
(b) 240 km
(c) 200 km
(d) 100 km
Solution:

Question 8.
In a mess, there was enough food for 200 students for 20 days. If 50 new students joined them, then the food will last for
(a) 15 days
(b) 16 days
(c) 17 days
(d) 18 days
Solution:

Question 9.
3 persons can paint a house in 8 days, then 4 persons can paint the same house in
(a) 5 days
(b) 6 days
(c) 7 days
(d) none of these
Solution:

Question 10.
A photograph of bacteria is enlarged 100000 times attains a length of 5 cm, then actual length of the bacteria is
(a) 0.00005 cm
(b) 5 × 10^-5
(c) 5 × 10^-7
(d) all of these
Solution:

Question 11.
A tree 12 metre high casts a shadow of length 8 metre. Height of the tree whose shadow is 6 metre in length is
(a) 6 m
(b) 9 m
(c) 15 m
(d) none of these
Solution:

Question 12.
If 5 pipes can fill the tank in 1 hour, then 4 pipes will fill the tank in
(a) 75 minutes
(b) 70 minutes
(c) 65 minutes
(d) none of these
Solution:

Question 13.
A tap fills a tank in 8 hours and another tap at the bottom empties it in 10 hours. If both work together, the tank will be filled in
(a) 18 hours
(b) 24 hours
(c) 36 hours
(d) 40 hours
Solution:

Value-Based Questions
Question 1.
The cost of fuel for running a train is proportional to the speed generated in km/h. It costs ₹40 per hour when train is moving with 20 km/h. What would be the cost of fuel per hour, if the train is moving with 60 km/h?
Keeping the safety and fuel prices in mind, state the values promoted in the question.
Solution:

Question 2.
A pipe can fill a tank in 9 hours. There is a leakage in the bottom of the tank due to which tank is filled in 12 hours. If the tank is full, how much time will leakage take to empty the tank? Should we repair the leakage tank? Should we repair the leakage of the tank immediately? What values are being promoted?
Solution:

Higher Order Thinking Skills (Hots)
Question 1.
If 8 labourers can earn ₹9000 in 15 days, how many labourers can earn ₹6300 in 7 days?
Solution:

Question 2.
Three typists working 8 hours a day type a document in 10 days. If only 2 typists are working, how many hours a day should they work to finish the job in 12 days?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 9 Direct and Inverse Variation Ex 9.3

Question 1.
A farmer can reap a field in 10 days while his wife can do it in 8 days (she does not waste time in smoking). If they work together, in how much time can they reap the field?
Solution:

Question 2.
A can-do \(\frac{1}{5}\)th of a certain work in 2 days and B can do \(\frac{2}{3}\)rd of it in 8 days. In how much time can they together complete the work?
Solution:

Question 3.
One tap fills a tank in 20 minutes and another tap fills it in 12 minutes. The tank being empty and if both taps are opened together, in how many minutes the tank will be full?
Solution:

Question 4.
A can do a work in 6 days and B can do it in 8 days. They worked together for 2 days and then B left the work. How many days will A require to finish the work?
Solution:

Question 5.
A can do a piece of work in 40 days. He works at it for 8 days and then B finishes the remaining work in 16 days. How long will they take to complete the work if they do it together?
Solution:

Question 6.
A and B separately do a work in 10 and 15 Solution: days respectively. They worked together for some days and then A completed the remaining work in 5 days. For how many days had A and B worked together?
Solution:

Question 7.
If 3 women or 5 girls take 17 days to complete a piece of work, how long will 7 women and 11 girls working together take to complete the work?
Solution:

Question 8.
A can do a job in 10 days while B can do it in 15 days. If they work together and earn ₹3500, how should they share the money?
Solution:

Question 9.
A, B and C can separately do a work in 2, 6 and 3 days respectively. Working together, how much time would they require to do it? If the work earns them ₹1960, how should they divide the money?
Solution:

Question 10.
A, B and C together can do a piece of work in 15 days, B alone can do it in 30 days and C alone can do it in 40 days. In how many days will A alone do the work?
Solution:

Question 11.
A, B and C working together can plough a field in \(4 \frac{4}{5}\) days. A and C together can do it in 8 days. How long would B working alone take to plough the field?
Solution:

Question 12.
A and B together can build a wall in 10 days; B and C working together can do it in 15 days; C and A together can do it in 12 days. How long will they take to finish the work, working altogether? Also find the number of days taken by each to do the ^ame work, working alone.
Solution:

Question 13.
A pipe can fill a tank in 12 hours. By mistake, a waste pipe in the bottom is left opened and the tank is filled in 16 hours. If the tank is full, how much time will the waste pipe take to empty it?
Solution:.

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 9 Direct and Inverse Variation Ex 9.2

Question 1.
Which of the following are in inverse variation?
(i) The number of students in a hostel and the consumption of food.
(ii) Time is taken by a train to cover a fixed distance and the speed of the train.
(iii) Area of land and its cost.
(iv) The number of people working and the time to complete the work.
(v) The quantity of rice and its cost.
Solution:

Question 2.
Observe the following tables and find which pair of variables (here x and y) are in inverse variation:

Solution:

Question 3.
Under the condition that the temperature remains constant, the volume of gas is inversely proportional to its pressure. If the volume of gas is 630 cubic centimetres at a pressure of 360 mm of mercury, then what will be the pressure of the gas, if its volume is 720 cubic centimetres at the same temperature?
Solution:

Question 4.
A packet of sweets was distributed among 20 children and each of them received 4 sweets. How many sweets will each child get, if the number of children is reduced by 4?
Solution:

Question 5.
Pooja has enough money to buy 36 oranges at the rate of ₹4.50 per orange. How many oranges she can buy if the price of each orange is increased by 90 paise?
Solution:

Question 6.
It takes 8 days for 12 men to construct a wall. How many men should be put on the job if it is required to be constructed in 6 days.?
Solution:

Question 7.
Eight taps through which water flows at the same rate can fill a tank in 27 minutes. If two taps go out of order, how long will the remaining taps take to fill the tank?
Solution:

Question 8.
A contractor undertook a contract to complete a part of a stadium in 9 months with a team of 560 persons. Later on, it was required to complete the job in 5 months. How many extra persons should he employ to complete the work?
Solution:

Question 9.
A batch of bottles were packed in 30 boxes with 10 bottles in each box. If the same batch is packed using 12 bottles in each box, how many boxes would be filled?
Solution:

Question 10.
Vandana takes 24 minutes to reach her school if she goes at a speed of 5 km/h. If she wants to reach school in 20 minutes, what should be her speed?
Solution:

Question 11.
A fort is provided with food for 80 soldiers to last for 60 days. Find how long would the food last if 20 additional soldiers join after 15 days.
Solution:

Question 12.
1200 soldiers in a fort had enough food for 28 days. After 4 days, some soldiers were sent to another fort and thus, the food lasted for 32 more days. How many soldiers left the fort?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 9 Direct and Inverse Variation Ex 9.1

Question 1.
Observe the following tables and find if x and y are directly proportional:
(i)

(ii)

Solution:

Question 2.
If x and y are in direct variation, complete the following tables:
(i)

(ii)

Solution:

Question 3.
If 8 metres cloth costs ₹250, find the cost of 5·8 metres of the same cloth.
Solution:

Question 4.
If a labourer earns ₹672 per week, how much will he earn in 18 days?
Solution:

Question 5.
If 175 dollars cost ₹7350, how many dollars can be purchased in ₹24024?
Solution:

Question 6.
If a car travels 67·5 km in 4·5 litres of petrol, how many kilometres will it travel in 26-4 litres of petrol?
Solution:

Question 7.
If the thickness of a pile of 12 cardboard sheets is 45 mm, then how many sheets of the same cardboard would be 90 cm thick?
Solution:

Question 8.
In a model of a ship, the mast (flagstaff) is 6 cm high, while the mast of the actual ship is 9 m high. If the length of the ship is 33 m, how long is the model of the ship?
Solution:

Question 9.
The mass of an aluminium rod varies directly with its length. If a 16 cm long rod has a mass of 192 g, find the length of the rod whose mass is 105 g.
Solution:

Question 10.
Anita has to drive from village A to village B. She measures a distance of 3.5 cm between these villages on the map. What is the actual distance between the villages if the map scale is 1 cm = 20 km?
Solution:

Question 11.
A 23 m 75 cm high water tank casts a shadow 20 m long. Find at the same time;
(i) the length of the shadow cast by a tree 9 m 50 cm high.
(ii) the height of the tree if the length of the shadow is 12 m.
Solution:

Question 12.
If 5 men or 7 women can earn ₹525 per day, how much would 10 men and 13 women will earn per day.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 8 Simple and Compound Interest Check Your Progress

Question 1.
Find the amount and the compound interest on ₹5000 for 2 years at 6% per annum interest payable yearly.
Solution:

Question 2.
Find the amount and the compounded interest on ₹7400 for 1 year at 5% per annum, interest payable half-yearly.
Solution:

Question 3.
Find the difference between C.I. and S.l. on a sum of ₹5000 for 2 years at 8% per annum payable yearly.
Solution:

Question 4.
Find the amount and compound interest on ₹10000 for \(1 \frac{1}{2}\) years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
Solution:

Question 5.
What sum invested for \(1 \frac{1}{2}\) years compounded half-yearly at the rate of 4% p.a. will amount to ₹ 132651?
Solution:

Question 6.
Find the time (in years) in which ₹ 12500 will produce ₹3246.40 as compound interest at 8% per annum, compounded annually.
Solution:

Question 7.
Find the amount and compound interest on ₹2500 in 2 years if the rate are 5% and 6% for the successive years.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths