M l aggarwal understanding icse mathematics class 8 Solutions for Chapter 9 direct and inverse variation

Observe the following tables and find if x and y are directly proportional

If x and y are in direct variation, complete the following tables:

If 8 meters cloth costs ₹250, find the cost of 5.8 meters of the same cloth

If a laborer earns ₹672 per week, how much will he earn in 18 days?

if 175 dollars cost ₹7350, how many dollars can be purchased in ₹24024?

If a car travels 67.5 km in 4.5 liters of petrol, how many kilometers will it travel in

26.4 liters of petrol?

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?

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?

The mass of an aluminum 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.

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?

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.

If 5 men or 7 women can earn ₹525 per day, how much 10 men and 13 women

would earn per day

Which of the following are in inverse variation?

(i) A number of students in a hostel and 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

Observe the following tables and find which pair of variables (here x and y) are in

inverse variation:

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 centimeters

at a pressure of 360 mm of mercury, then what will be the pressure of the gas, if its

volume is 720 cubic centimeters at the same temperature?

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?

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?

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?

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?

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?

A batch of bottles was 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?

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?

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.

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?

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?

A can-do 1/5th of a certain work in 2 days and B can do 2/3rd of it in 8 days. In how much time can they together complete the work?

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

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?

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?

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.

how many days had A and B worked together?

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?

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?

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 ₹960, how should they divide the money?

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?

A, B, and C working together can plogh a field in 4 4/5 days. A and C together can do it in 8 days. How long would B working alone take to plough the field?

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 same work, working alone.

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?