ML Aggarwal Direct and Inverse Variation Exe-9.2 Class 8 ICSE Ch-9 Maths Solutions. We Provide Step by Step Answer of  Exe-9.2 Questions for Direct and Inverse Variation as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-8.

## ML Aggarwal Direct and Inverse Variation Exe-9.2 Class 8 ICSE Maths Solutions

 Board ICSE Publications Avichal Publishig Company (APC) Subject Maths Class 8th Chapter-9 Direct and Inverse Variation Writer ML Aggarwal Book Name Understanding Topics Solution of Exe-9.2 Questions Edition 2023-2024

### Direct and Inverse Variation Exe-9.2

ML Aggarwal Class 8 ICSE Maths Solutions

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#### Question 1. Which of the following are 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.

(i),(ii) and (iv) are inverse variations as here xy= constant.

### Direct and Inverse Variation Exe-9.2

ML Aggarwal Class 8 ICSE Maths Solutions

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

(i)

 x 90 60 45 30 20 y 10 15 20 30 45

(ii)

 x 75 45 30 20 10 y 10 30 25 35 65

Since x and y are in inverse variation

Hence xy is constant

(i) xy = 90 × 10 = 900

xy = 60 × 15 = 900

xy = 45 × 20 = 900

xy = 30 × 30 = 900

xy = 20 × 45 = 900

We see that in every case, xy is constant.

∴ It is in inverse variation.

(ii) xy = 75 × 10 = 750

xy = 45 × 30 = 1350

xy = 30 × 25 = 750

xy = 20 × 35 = 700

xy= 10 × 65 =650

We see that in each case xy is not same.

∴ It is not in inverse variation.

#### 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?

Temperature remains constant and volume of gas is inversely proportional to its pressure.

So, let ‘x’ = Volume of gas = 630 cubic cm

and ‘y’ = Pressure = 360 mm

Let pressure of gas be an ‘mm’

and their volume = 720 cubic cm

So, 630 × 360 = a × 720

a = (630 × 360)/720

= 315

∴ Pressure of gas is 315 mm of mercury.

#### 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?

x1 = 20 and y1 = 4

x2 = 16 and y2 = ?

x1y1 = x2y2

20 × 4 = 16 × y2

y2 = (20 × 4)/16

= 5

So, Each child will get 5 sweets.

#### 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?

Cost of one orange=Rs.4.50

Therefore cost of 36 oranges=Rs 4.50*36=Rs 162

New price of one orange =Rs.4.50*+0.90=rs.5.40

therefore In Rs. 162, oranges can be bought =​ = 162/5.40 =30

Hence no. of oranges available=30

#### 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.?

12 men constructed a wall in 8 days.

therefore man construct a wall in= 12*8 days.

Therefore man construct a wall in =​ (12 × 8)/6 days

=16 days.

#### 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?

Eight taps through which water flows at same rate can fill a tank in = 27 minutes.

So, taps through which water flows can fill a tank in = 27 × 8 minutes

Two taps go out of order then, remaining taps = 8 – 2 = 6 taps

∴ 6 taps through which water flows can fill a tank in = (27 × 8)/6 minutes

= 36 minutes

#### 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?

To complete a work ,560 persons were employed  for 9 months,

but to complete the same work is to be completed in 5 months ,

so person will be=​ (560 × 9)/5

= 1008 person

Therefore more persons to be required = 1008-560

=468 persons.

#### 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?

A batch of bottles were packed in 30 boxes with 10 bottles in each box.

No. of boxes required to fill 12 bottles at each box = (30 × 10)/12

= 25 boxes

#### 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?

Vandana takes 21 mins. to reach her school with a speed of 5 km/hr.

To reach the school in 20 mins, she will go with a speed =​

(24×5)/20

= 6 km/h

#### 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.

After 15 days , the food is sufficient for 80 students  for(60-15)days i,e. 45 days

After 15 days, 20 additional soldiers  join the fort =80+20=100

Since for 80 soldiers , the food is sufficient for=45 days

Therefore for 1 soldier , the food is sufficient for=(80 × 45)days

Hence, for 100 soldiers ,the food is sufficient for =(80 × 45)/100 days

=36 days

#### 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?

No. of total days=28

Days spent=4

Therefore no. of days left =28-4=24

Therefore no. of soldiers=1200

and the food lasted for=32 days

Therefore in 24 days, the food is sufficient for =1200 soldiers

In 1 day, the food will be sufficient for = 1200 × 24

In 32 days, the food will be sufficient for = (1200 × 24) = 900 persons

So, Number of soldiers sent to another fort = 1200 – 900

= 300 persons

— End of Direct and Inverse Variation Exe-9.2 Class 8 ICSE Maths Solutions :–