# RS Aggarwal Class 8 Math Twelfth Chapter Direct Inverse Proportions Exercise 12A Solution

## EXERCISE 12A

(1) Observe the table given below and in each one find whether x and y are proportional:

(i)

 x 3 5 8 11 26 y 9 15 24 33 78 ∴ x and y are directly proportional.

(ii)

 x 2.5 4 7.5 10 14 y 10 16 30 40 42

Solution: We have: ∴ x and y are not directly proportional.

(iii)

 X 5 7 9 15 18 25 y 15 21 27 60 72 75

Solution: We have: ∴ x and y are not directly proportional.

(2) If x and y are directly proportional, find the values of x1, and x2 and y1 in the table given below:

 x 3 x1 x2 10 y 72 120 192 y1

Solution: Since x and y are directly proportional. We have: x1=5, x2 = 8 and y1 = 240.

(3) A truck covers a distance of 510 km in 34 litres of diesel. How much distance would it cover in 20 litres of diesel?

Solution: Let the required distance be x km. Then, we have:

 Quantity of petrol(in lit) 34 20 Distance (in km) 510 x

Clearly, less is the quantity of diesel consumed, less is the distance covered. So, it is a case of direct proportion. ∴ Required distance is 300 km.

(4) A taxi charges a fare of Rs 2550 for a journey of 150 km. How much would it charge for a journey of 124 km?

Solution: Let the required charges be Rs x. Then we have:

 Distance (in Km) 150 124 Charges of fare (in Rs) 2550 x

Clearly, less is the cost, less is the distance of journey.

So, it is a case of direct proportion. ∴ Required amount of charges Rs 2108.

(5) A loaded truck covers 16 km in 25 minutes. At the same speed, how far can it travel in 5 hours?

Solution: Here, 5 hours = (5×60) = 300 minutes

Let the required distance be x km. Then, we have:

 Distance (in Km) 16 x Time (in minutes) 25 300

Clearly, more distance will be covered more time.

So, it is a case of direct proportion. ∴ Required distance is 192 Km.

(6) If 18 dolls cost Rs 630, how many dolls can be bought for Rs 455?

Solution: Let the number required dolls be x. Then, we have:

 Number of dolls 18 x Cost of dolls (Rs) 630 455

Clearly, more dolls will be more cost. So it is case of direct proportion. (7) If  9 kg of sugar costs Rs 238.50, how much sugar can be bought for Rs 371?

Solution: Let the required quantity of sugar be x kg. Then, we have:

 Quantity of sugar (in kg) 9 x Cost of sugar (in Rs) 238.5 371

Clearly, more sugar will be more cost. So it is case of direct proportion. ∴ The required quantity of sugar is 14 kg.

(8) The cost of 15 metres of a cloth is Rs 981. What length of this cloth can be purchased for Rs 1308?

Solution: Let the length of required cloth be x metres. Then, we have:

 Length of the cloth (in metre) 15 x Cost of cloth (in Rs) 981 1308

Clearly, more cloth will be more cost. So it is case of direct proportion. ∴ The required length of the cloth is 20 metres.

(9) In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 15 m high. If the length of the ship is 35 metres, how long is the model ship?

Solution: Let the length of the model ship be x cm.

Here, 15m = 1500 cm and 35 m = 3500 cm

 Length of model ship(cm) 9 x Length of actual ship (cm) 1500 3500 ∴ The required length of the model ship is 21 cm.

(10) In 8 days, the earth picks up (6.4×107) kg of dust from the atmosphere. How much dust will it pick up in 15 days?

Solution: Let the required amount of dust be x kg.

 Time (Days) 8 15 Amount of dust (in Kg) 6.4×107 x

More days will be more dust. So, it is a case of direct proportion. ∴ The required amount of dust is 1.2 × 108.

(11) A car is travelling at the average speed of 50 km/hr. How much distance would it travel in 1 hour 12 minutes?

Solution: Let the required distance be x km.

Here, 1 hour 12 minutes = 72 minutes

 Time (In minutes) 60 72 Distance (In Km) 50 x

More time will be more distance. So, it is case of direct proportion. ∴ The required distance is 60 km.

(12) Ravi walks at the uniform rate of 5 km/hr. What distance would he cover in 2 hours 24 minutes?

Solution: Let the required distance will be x km.

Here, 2 hours 24 minutes = 144 minutes

 Distance (in Km) 5 x Time (minutes) 60 144

More time will be more distance. So, it is case of direct proportion. ∴ The required distance is 12 km.

(13) If the thickness of a pile of 12 cardboards is 65 mm, find the thickness of a pile of 312 such cardboards.

Solution: Let the thickness of pile be x mm.

 Thickness of pile (in mm) 65 x Number of card boards 12 312

More cardboard will be more thickness. So, it is case of direct proportion. (14) 11 men can dig 6(3/4) metre long trench in one day. How many men should be employed for digging 27 metre long trench of the same type in one day? ∴ The required number of men is 44.

(15) Reenu types 540 words during half an hour. How many words would she type in 8 minutes?

Solution: Here, half an hour = 30 minutes

Let the number of words be x.

 Time (in minutes) 30 8 Number of words 540 x

Less time will be she type Less words. So, it is case of direct proportion. ∴ The required number of words is 144.

Updated: December 15, 2018 — 12:33 pm