Rs Aggarwal 2018 Solutions for Class 8 Math Chapter 12 Direct And Inverse Proportions are provided here with simple step-by-step explanations. These solutions for Direct And Inverse Proportions are extremely popular among Class 8 students for Math Direct And Inverse Proportions Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2018 Book of Class 8 Math Chapter 12 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2018 Solutions. All Rs Aggarwal 2018 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

#### Question 1:

Observe the tables 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

(ii)
 x 2.5 4 7.5 10 14 y 10 16 30 40 42

(iii)
 x 5 7 9 15 18 25 y 15 21 27 60 72 75

(i)

(ii)

(iii)

#### Question 2:

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

 x 3 x1 x2 10 y 72 120 192 y1

#### Question 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?

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

 Quantity of diesel (in litres) 34 20 Distance (in km) 510 x

Clearly, the less the quantity of diesel consumed, the less is the distance covered.
So, this is a case of direct proportion.

Therefore, the required distance is 300 km.

#### Question 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?

Let the charge for a journey of 124 km be â‚¹x.

 Price(in â‚¹) 2550 x Distance(in km) 150 124
More is the distance travelled, more will be the price.
So, it is a case of direct proportion.
$\therefore \frac{2550}{150}=\frac{x}{124}\phantom{\rule{0ex}{0ex}}⇒x=\frac{2550×124}{150}=2108$
Thus, the taxi charges â‚¹2,108 for the distance of 124 km.

#### Question 5:

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

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

 Distance (in km) 16 x Time (in min) 25 300

Clearly, the more the time taken, the more will be the distance covered.

So, this is a case of direct proportion.

Therefore, the required distance is 192 km.

#### Question 6:

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

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

 No of dolls 18 x Cost of dolls (in rupees) 630 455

Clearly, the less the amount of money, the less will be the number of dolls bought.
So, this is a case of direct proportion.

Therefore, 13 dolls can be bought for Rs 455.

#### Question 7:

If 9 kg of sugar costs â‚¹ 238.50, how much sugar can be bought for â‚¹ 371?

Let the quantity of sugar bought for â‚¹371 be x kg.

 Quantity(in kg) 9 x Price(in â‚¹) 238.5 371
The price increases as the quantity increases. Thus, this is a case of direct proportion.
$\therefore \frac{9}{238.50}=\frac{x}{371}\phantom{\rule{0ex}{0ex}}⇒x=\frac{9×371}{238.50}=14$
Thus, the quantity of sugar bought for â‚¹371 is 14 kg.

#### Question 8:

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

Let the length of cloth be x m. Then, we have:
â€‹

 Length of cloth (in metres) 15 x Cost of cloth (in rupees) 981 1308

Clearly, more length of cloth can be bought by more amount of money.
So, this is a case of direct proportion.

Therefore, 20 m of cloth can be bought for Rs 1,308.

#### Question 9:

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

Let x m be the length of the model of the ship. Then, we have:

 Length of the mast (in cm) Length of the  ship (in cm) Actual ship 1500 3500 Model of the ship 9 x

Clearly, if the length of the actual ship is more, then the length of the model ship will also be more.
So, this is a case of direct proportion.

Therefore, the length of the model of the ship is 21 cm.

#### Question 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?

Let x kg be the required amount of dust. Then, we have:

 No. of days 8 15 Dust (in kg) $6.4×{10}^{7}$ x

Clearly, more amount of dust will be collected in more number of days.
So, this is a case of direct proportion.

Therefore, 12,00,00,000 kg of dust will be picked up in 15 days.

#### Question 11:

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

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

 Distance covered (in km) 50 x Time (in min) 60 72

Clearly, more distance will be covered in more time.
So, this is a case of direct proportion.

Therefore, the distance travelled by the car in 1 h 12 min is 60 km.

#### Question 12:

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

Let x km be the required distance covered by Ravi in 2 h 24 min.
Then, we have:

 Distance covered (in km) 5 x Time (in min) 60 144

Clearly, more distance will be covered in more time.
So, this is a case of direct proportion.
$\mathrm{Now},\frac{5}{60}=\frac{x}{144}\phantom{\rule{0ex}{0ex}}⇒x=\frac{5×144}{60}\phantom{\rule{0ex}{0ex}}⇒x=12\phantom{\rule{0ex}{0ex}}$

Therefore, the distance covered by Ravi in 2 h 24 min is 12 km.

#### Question 13:

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

Let x mm be the required thickness. Then, we have:

 Thickness of cardboard (in mm) 65 x No. of cardboards 12 312

Clearly, when the number of cardboard is more, the thickness will also be more.
So, it is a case of direct proportion.

Therefore, the thickness of the pile of 312 cardboards is 1690 mm.

#### Question 14:

11 men can dig $6\frac{3}{4}$-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?

Let x be the required number of men.

Then, we have:

 Number of men 11 x Length of trench (in metres) $\frac{27}{4}$ 27

Clearly, the longer the trench, the greater will be the number of men required.
So, it is a case of direct proportion.

Therefore, 44 men should be employed to dig a trench of length 27 m.

#### Question 15:

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

Let Reenu type x words in 8 minutes.

 No. of words 540 x Time taken (in min) 30 8

Clearly, less number of words will be typed in less time.
So, it is a case of direct proportion.
$\mathrm{Now},\frac{540}{30}=\frac{x}{8}\phantom{\rule{0ex}{0ex}}⇒x=\frac{540×8}{30}\phantom{\rule{0ex}{0ex}}⇒x=144\phantom{\rule{0ex}{0ex}}$

Therefore, Reenu will type 144 words in 8 minutes.

#### Question 1:

Observe the tables given below and in each case find whether x and y are inversely proportional:
(i)

 x 6 10 14 16 y 9 15 21 24

(ii)
 x 5 9 15 3 45 y 18 10 6 30 2

(iii)
 x 9 3 6 36 y 4 12 9 1

(i)

(ii)

(iii)

#### Question 2:

If x and y are inversely proportional, find the values of x1, x2, y1 and y2 in the table given below:

 x 8 x1 16 x2 80 y y1 4 5 2 y2

#### Question 3:

If 35 men can reap a field in 8 days, in how many days can 20 men reap the same field?

Let x be the required number of days. Then, we have:

 No. of days 8 x No. of men 35 20

Clearly, less men will take more days to reap the field.
So, it is a case of inverse proportion.

Therefore, 20 men can reap the same field in 14 days.

#### Question 4:

12 men can dig a pond in 8 days. How many men can dig it in 6 days?

Let x be the required number of men. Then, we have:

 No. of days 8 6 No. of men 12 x

Clearly, more men will require less number of days to dig the pond.
So, it is a case of inverse proportion.

Therefore, 16 men can dig the pond in 6 days.

#### Question 5:

6 cows can graze a field in 28 days. How long would 14 cows take to graze the same field?

Let x be the number of days. Then, we have:

 No. of days 28 x No. of cows 6 14

Clearly, more number of cows will take less number of days to graze the field.
So, it is a case of inverse proportion.

Therefore, 14 cows will take 12 days to graze the field.

#### Question 6:

A car takes 5 hours to reach a destination by travelling at the speed of 60 km/hr. How long will it take when the car travels at the speed of 75 km/hr?

Let x h be the required time taken. Then, we have:

 Speed (in km/h) 60 75 Time (in h) 5 x

Clearly, the higher the speed, the lesser will be the the time taken.
So, it is a case of inverse proportion.

Therefore, the car will reach its destination in 4 h if it travels at a speed of 75 km/h.

#### Question 7:

A factory requires 42 machines to produce a given number of articles in 56 days. How many machines would be required to produce the same number of articles in 48 days?

Let x be the number of machines required to produce same number of articles in 48.
Then, we have:

 No. of machines 42 x No. of days 56 48

Clearly, less number of days will require more number of machines.
So, it is a case of inverse proportion.

Therefore, 49 machines would be required to produce the same number of articles in 48 days.

#### Question 8:

7 teps of the same size fill a tank in 1 hour 36 minutes. How long will 8 taps of the same size take to fill the tank?

Let x be the required number of taps. Then, we have:
1 h = 60 min
i.e., 1 h 36 min = (60+36) min = 96 min

 No. of taps 7 8 Time (in min) 96 x

Clearly, more number of taps will require less time to fill the tank.
So, it is a case of inverse proportion.

Therefore, 8 taps of the same size will take 84 min or 1 h 24 min to fill the tank.

#### Question 9:

8 taps of the same size fill a tank in 27 minutes. If two taps go out of order, how long would the remaining taps take to fill the tank?

Let x min be the required number of time. Then, we have:

 No. of taps 8 6 Time (in min) 27 $x$

Clearly, less number of taps will take more time to fill the tank .
So, it is a case of inverse proportion.

Therefore, it will take 36 min to fill the tank.

#### Question 10:

A farmer has enough food to feed 28 animals in his cattle for 9 days. How long would the food last, if there were 8 more animals in his cattle?

Let x be the required number of days. Then, we have:

 No. of days 9 x No. of animals 28 36

Clearly, more number of animals will take less number of days to finish the food.
So, it is a case of inverse proportion.

Therefore, the food will last for 7 days.

#### Question 11:

A garrison of 900 men had provisions for 42 days. However, a reinforcement of 500 men arrived. For how many days will the food last now?

Let x be the required number of days. Then, we have:

 No. of men 900 1400 No. of days 42 x

Clearly, more men will take less number of days to finish the food.
So, it is a case of inverse proportion.

Therefore, the food will now last for 27 days.

#### Question 12:

In a hostel, 75 students had food provision for 24 days. If 15 students leave the hostel, for how many days would the food provision last?

Let x be the required number of days. Then, we have:

 No. of students 75 60 No. of days 24 x

Clearly, less number of students will take more days to finish the food.
So, it is a case of inverse proportion.

Therefore, the food will now last for 30 days.

#### Question 13:

A school has 9 periods a day each of 40 minutes duration. How long would each period be, if the school has 8 periods a day, assuming the number of school hours to be the same?

Let x min be the duration of each period when the school has 8 periods a day.

 No. of periods 9 8 Time (in min) 40 x

Clearly, if the number of periods reduces, the duration of each period will increase.
So, it is a case of inverse proportion.

Therefore, the duration of each period will be 45 min if there were eight periods a day.

#### Question 14:

If x and y vary inversely and x = 15 when y = 6, find y when x = 9.

 $x$ 15 9 $y$ 6 ${y}_{1}$

∴ Value of $y=10$, when x =9

#### Question 15:

If x and y vary inversely and x = 18 when y = 8, find x when y = 16.

 $x$ 18 ${x}_{1}$ $y$ 8 16

∴ Value of $x=9$

#### Question 1:

If 14 kg of pulses cost â‚¹ 882, what is the cost of 22 kg of pulses?
(a) â‚¹ 1254
(b) â‚¹ 1298
(c) â‚¹ 1342
(d) â‚¹ 1386

Let 22 kg of pulses cost â‚¹x.

 Quantity(in kg) 14 22 Price(in â‚¹) 882 x
As the quantity increases, the price also increases. So, it is a case of direct proportion.
$\therefore \frac{14}{882}=\frac{22}{x}\phantom{\rule{0ex}{0ex}}⇒x=\frac{22×882}{14}=1386$
Thus, the cost of 22 kg of pulses is â‚¹1,386.

Hence, the correct answer is option (d).

#### Question 2:

If 8 oranges cost â‚¹ 52, how many oranges can be bought for â‚¹ 169?
(a) 13
(b) 18
(c) 26
(d) 24

Let the number of oranges that can be bought for â‚¹169 be x.

 Quantity 8 x Price(in â‚¹) 52 169
As the quantity increases the price also increases. So, this is a case of direct proportion.
$\therefore \frac{8}{52}=\frac{x}{169}\phantom{\rule{0ex}{0ex}}⇒x=\frac{8×169}{52}=26$
Thus, 26 oranges can be bought for â‚¹169.

Hence, the correct answer is option (c).

#### Question 3:

A machine fills 420 bottles in 3 hours. How many bottles will it fill in 5 hours?
(a) 252
(b) 700
(c) 504
(d) 300

(b) 700

Let x be the number of bottles filled in 5 hours.

 No. of bottles 420 $x$ Time (h) 3 5

More number of bottles will be filled in more time.

Therefore, 700 bottles would be filled in 5 h.

#### Question 4:

A car is travelling at a uniform speed of 75 km/hr. How much distance will it cover in 20 minutes?
(a) 25 km
(b) 15 km
(c) 30 km
(d) 20 km

(a) 25 km

Let x km be the required distance.
Now, 1 h = 60 min

 Distance (in km) 75 $x$ Time (in min) 60 20

Less distance will be covered in less time.

#### Question 5:

The weight of 12 sheets of a thick paper is 40 grams. How many sheets would weight 1 kg?
(a) 480
(b) 360
(c) 300
(d) none of these

(c) 300
Let x sheets weigh 1 kg.
Now, 1 kg = 1000 g

 No. of sheets 12 $x$ Weight (in  g) 40 1000

#### Question 6:

A pole 14 m high casts a shadow of 10 m. At the same time, what will be the height of a tree, the length of whose shadow is 7 metres?
(a) 20 m
(b) 9.8 m
(c) 5 m
(d) none of these

(b) 9.8 m
Let x m be the height of the tree.

 Height of object 14 $x$ Length of shadow 10 7

The more the length of the shadow, the more will be the height of the tree.

Therefore, a 9.8 m tall tree will cast a shadow of length 7 m.

#### Question 7:

A photograph of a bacteria enlarged 50000 times attains a length of 5 cm. The actual length of bacteria is
(a) 1000 cm
(b) 10−3 cm
(c) 10−4 cm
(d) 10−2 cm

(c)
Let x cm be the actual length of the bacteria.
The larger the object, the larger its image will be.

Hence, the actual length of the bacteria is â€‹.

#### Question 8:

6 pipes fill a tank in 120 minutes, then 5 pipes will fill it in
(a) 100 min
(b) 144 min
(c) 140 min
(d) 108 min

(b) 144 min
Let x min be the time taken by 5 pipes to fill the tank.

 No. of pipes 6 5 Time (in min) 120 $x$

Therefore, 5 pipes will take 144 min to fill the tank.

#### Question 9:

3 persons can build a wall in 4 days, then 4 persons can build it in
(a) $5\frac{1}{3}$ days
(b) 3 days
(c) $4\frac{1}{3}$ days
(d) none of these

(b) 3 days
Let x be number of days taken by 4 persons to build the wall.

 No. of persons 3 4 No. of days 4 $x$

More number of persons will take less time to build the wall.
So, it is a case of inverse proportion.

Therefore, 4 persons can build the wall in 3 days.

#### Question 10:

A car takes 2 hours to reach a destination by travelling at 60 km/hr. How long will it take while travelling at 80 km/hr?
(a) 1 hr 30 min
(b) 1 hr 40 min
(c) 2 hrs 40 min
(d) none of these

(a) 1 h 30 min
Let x h be the time taken by the car travelling at 80 km/hr.

 Speed (km/h) 60 80 Time (in h) 2 $x$

#### Question 1:

350 boxes can be placed in 25 cartons. How many boxes can be placed in 16 cartons?

Let x be the required number of boxes.

 No. of boxes 350 $x$ No. of cartons 25 16

Less number of boxes will require less number of cartons.
So, it is a case of direct proportion.

∴ 224 boxes can be placed in 16 cartoons.

#### Question 2:

The cost of 140 tennis balls is Rs 4900. Find the cost of 2 dozen such balls.

Let Rs x be the cost of 24 tennis balls.

 No. of balls 140 24 Cost of balls 4900 $x$

More tennis balls will cost more.

∴ The cost of 2 dozen tennis balls is Rs 840.

#### Question 3:

The railway fare for 61 km is Rs 183. Find the fare for 53 km.

Let Rs x be the railway fare for a journey of distance 53 km.

 Distance (in km) 61 53 Railway fare (in rupees) 183 $x$

The lesser the distance, the lesser will be the fare.
So, it is a case of direct proportion .

The railway fare for a journey of distance 53 km is Rs 159.

#### Question 4:

10 people can dig a trench in 6 days. How many people can dig it in 4 days?

Let x people dig the trench in 4 days.

 No. of people 10 $x$ No. of days 6 4

More people will take less number of days to dig the trench. Hence, this is a case of inverse proportion.

∴ 15 people can dig the trench in 4 days.

#### Question 5:

30 men can finish a piece of work in 28 days. How many days will be taken by 21 men to finish it?

Let x be the number of days taken by 21 men to finish the piece of work.

 No. of men 30 21 No. of days 28 $x$

More men will take less time to complete the work.
So, this is a case of inverse proportion.

∴ 21 men will take 40 days to finish the piece of work.

#### Question 6:

A garrison of 200 men had provisions for 45 days. After 15 days, 40 more men join the garrison. Find the number of days for which the remaining food will last.

Clearly, the remaining food is sufficient for 200 men for (45 − 15), i.e., 30 days.
Total number of men = 200 + 40 = 240
Let the remaining food last for x days.

 No. of men 200 240 No. of days 30 $x$

Clearly, more men will take less number of days to finish the food.
So, it is a case of inverse proportion.

∴ The remaining food will last for 25 days.

#### Question 7:

Mark (âœ“) against the correct answer:
6 pipes can fill a tank in 24 minutes. One pipe can fill it in
(a) 4 minutes
(b) 30 minutes
(c) 72 minutes
(d) 144 minutes

(d) 144 minutes

Let one pipe take x min to fill the tank.

 No. of pipe 6 1 Time(in min) 24 $x$

Clearly, one pipe will take more time to fill the tank.
So, it is a case of inverse proportion.

∴ One pipe can fill the tank in 144 minutes.

#### Question 8:

Mark (âœ“) against the correct answer:
14 workers can build a wall in 42 days. One worker can build it in
(a) 3 days
(b) 147 days
(c) 294 days
(d) 588 days

(d) 588 days
Let one worker take x days to build the wall.

 No. of workers 14 1 No. of days 42 $x$

Clearly, one worker will take more days to finish the work.
So, it is a case of inverse proportion.

∴ One worker can build the wall in 588 days.

#### Question 9:

Mark (âœ“) against the correct answer:
35 men can reap a field in 8 days. In how many days can 20 men reap it?
(a) 14 days
(b) 28 days
(c) $87\frac{1}{2}$ days
(d) none of these

(a) 14 days
Let 20 men take x days to reap the field.

 No. of days 8 $x$ No. of men 35 20

Clearly, less number of men will take more days.
So, it is a case of inverse proportion.

∴ 20 men can reap the field in 14 days.

#### Question 10:

Mark (âœ“) against the correct answer:
A car is travelling at an average speed of 60 km per hour. How much distance will it cover in 1 hour 12 minutes?
(a) 50 km
(b) 72 km
(c) 63 km
(d) 67.2 km

(b) 72 km
Let x km be the distance covered in 1 h 12 min.
Now, 1 h 12 min = (60+12) min = 72 min

 Distance(in km) 60 $x$ Time(in min) 60 72

More distance will be covered in more time.
So, it is a cas of direct proportion.

∴ The car will cover a distance of 72 $\mathrm{km}$ in 1 h 12 min.â€‹

#### Question 11:

Mark (âœ“) against the correct answer:
Rashmi types 510 words in half an hour. How many words would she type in 10 minutes?
(a) 85
(b) 150
(c) 170
(d) 153

(c) 170 words

Let x be the number of words typed by Rashmi in 10 minutes.

 No. of words 510 $x$ Time(in min) 30 10

Less time will be taken to type less number of words.
So, it is a case of direct variation.

∴ Rashmi will type 170 words in 10 minutes.

#### Question 12:

Mark (âœ“) against the correct answer:
x and y vary directly. When x = 3, then y = 36. What will be the value of x when y = 96?
(a) 18
(b) 12
(c) 8
(d) 4

(c) 8

 $x$ 3 ${x}_{1}$ $y$ 36 96

∴ Value of $x=8$

#### Question 13:

Mark (âœ“) against the correct answer:
x and y vary inversely. When x = 15, then y = 6. What will be the value of y when x = 9?
(a) 10
(b) 15
(c) 54
(d) 135

(a) 10

 $x$ 15 9 $y$ 6 ${y}_{1}$

∴ Value of y = 10, when x = 9.

#### Question 14:

Fill in the blanks.
(i) If 3 persons can do a piece of work in 4 days, then 4 persons can do it in ......... days.
(ii) If 5 pipes can fill  tank in 144 minutes, then 6 pipes can fill it in ......... minutes.
(iii) A car covers a certain distance in 1 hr 30 minutes at 60 km per hour. If it moves at 45 km per hour, it will take ......... hours.
(iv) If 8 oranges cost Rs 20.80, the cost of 5 oranges is Rs .........
(v) The weight of 12 sheets of a paper is 50 grams. How many sheets will weigh 500 grams?

(i)
Let x be the number of days taken by 4 persons to complete the work.

 No. of days 4 $x$ No. of persons 3 4

Clearly, more workers will take less number of days.
So, it is a case of inverse proportion.

Therefore, 4 persons can do the piece of work in 3 days.

(ii)
Let x min be the time taken by 6 pipes to fill the tank.
 No. of pipes 5 6 Time (in min) 144 $x$

Clearly, more number of pipes will take less time to fill the tank.
So, it is a case of inverse proportion.

∴ 6 pipes can fill the tank in 120 min.

(iii)
Let x min be the time taken by the car travelling at 45 km/h.
Now, 1 h 30 min = (60+30) min
 Speed(in km/hr) 60 45 Time(in min) 90 $x$

Clearly, a car travelling at a less speed will take more time.
So, it is a case of inverse proportion.

∴ The car will take 2 h if it travels at a speed of 45 km/h.

(iv)
Let Rs x be the cost of 5 oranges.
 No. of oranges 8 5 Cost of oranges 20.8 $x$

Clearly, less number of oranges will cost less.
So, it is a case of direct variation.

∴ The cost of 5 oranges is Rs 13.

(v)
Let x be the number of sheets that weigh 500 g.
 No. of sheets 12 $x$ Weight(in grams) 50 500

More number of sheets will weigh more.
So, it is a case of direct variation.

∴ 120 sheets will weigh 500 g.

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