RD Sharma Solutions for Class 8 Math Chapter 10 Direct And Inverse Variations are provided here with simple step-by-step explanations. These solutions for Direct And Inverse Variations are extremely popular among class 8 students for Math Direct And Inverse Variations Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RD Sharma Book of class 8 Math Chapter 10 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RD Sharma Solutions. All RD Sharma Solutions for class 8 Math are prepared by experts and are 100% accurate.

#### Question 1:

In which of the following tables x and y vary inversely:
(i)

 x 4 3 12 1 y 6 8 2 24

(ii)
 x 5 20 10 4 y 20 5 10 25

(iii)
 x 4 3 6 1 y 9 12 8 36

(iv)
 x 9 24 15 3 y 8 3 4 25

#### Question 2:

It x and y vary inversely, fill in the following blanks:
(i)

 x 12 16 ... 8 ... y ... 6 4 ... 0.25

(ii)
 x 16 32 8 128 y 4 ... ... 0.25

(iii)
 x 9 ... 81 243 y 27 9 ... 1

#### Question 3:

Which of the following quantities vary inversely as each other?
(i) The number of x men hired to construct a wall and the time y taken to finish the job.
(ii) The length x of a journey by bus and price y of the ticket.
(iii) Journey (x km) undertaken by a car and the petrol (y litres) consumed by it.

(i) If the number of men is more, the time taken to construct a wall will be less. Therefore, it is in inverse variation.
(ii) If the length of a journey is more, the price of the ticket will also be more. Therefore, it is not in inverse variation.
(iii) If the length of the journey is more, the amount of petrol consumed by the car will also be more. Therefore, it is not in inverse variation.
Thus, only (i) is in inverse variation.

#### Question 4:

It is known that for a given mass of gas, the volume v varies inversely as the pressure p. Fill in the missing entries in the following table:

 v (in cm3) ... 48 60 ... 100 ... 200 p (in atmospheres) 2 ... 3/2 1 ... 1/2 ...

#### Question 5:

If 36 men can do a piece of work in 25 days, in how many days will 15 men do it?

Let x be the number of days in which 15 men can do a piece of work.

 Number of men 36 15 Number of days 25 x

#### Question 6:

A work force of 50 men with a contractor can finish a piece of work in 5 months. In how many months the same work can be completed by 125 men?

Let x be the number days required to complete a piece of work by 125 men.

 Number of men 50 125 Months 5 x

#### Question 7:

A work-force of 420 men with a contractor can finish a certain piece of work in 9 months. How many extra men must he employ to complete the job in 7 months?

Let x be the extra number of men employed to complete the job in 7 months.

 Number of men 420 x Months 9 7

#### Question 8:

1200 men can finish a stock of food in 35 days. How many more men should join them so that the same stock may last for 25 days?

 Number of men 1200 x Days 35 25

Let x be the number of additional men required to finish the stock in 25 days.

#### Question 9:

In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last?

 Number of girls 50 80 Number of days 40 x

#### Question 10:

A car can finish a certain journey in 10 hours at the speed of 48 km/hr. By how much should its speed be increased so that it may take only 8 hours to cover the same distance?

Let the increased speed be x km/h.

 Time (in h) 10 8 Speed (km/h) 48 x+48

#### Question 11:

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

 Number of soldiers 1200 1200-x Number of days for which food lasts 24 32

#### Question 12:

Three spraying machines working together can finish painting a house in 60 minutes. How long will it take for 5 machines of the same capacity to do the same job?

Let the time taken by 5 spraying machines to finish a painting job be x minutes.

 Number of machines 3 5 Time (in minutes) 60 x

#### Question 13:

A group of 3 friends staying together, consume 54 kg of wheat every month. Some more friends join this group and they find that the same amount of wheat lasts for 18 days. How many new members are there in this group now?

Let x be the number of new members in the group.

 Number of members 3 x Number of days 30 18

#### Question 14:

55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days?

Let x be the number of cows that can graze the field in 10 days .

 Number of days 16 10 Number of cows 55 x

#### Question 15:

18 men can reap a field in 35 days. For reaping the same field in 15 days, how many men are required?

Let the number of men required to reap the field in 15 days be x.

 Number of days 35 15 Number of men 18 x

#### Question 16:

A person has money to buy 25 cycles worth Rs 500 each. How many cycles he will be able to buy if each cycle is costing Rs 125 more?

Let x be the number of cycles bought if each cycle costs Rs 125 more.

 Cost of a cycle (in Rs) 500 625 Number of  cycles 25 x

#### Question 17:

Raghu has enough money to buy 75 machines worth Rs 200 each. How many machines can he buy if he gets a discount of Rs 50 on each machine?

Let x be the number of machines he can buy if a discount of Rs. 50 is offered on each machine.

 Number of machines 75 x Price of each machine (in Rs) 200 150

#### Question 18:

If x and y vary inversely as each other and
(i) x = 3 when y = 8, find y when x = 4
(ii) x = 5 when y = 15, find x when y = 12
(iii) x = 30, find y when constant of variation = 900.
(iv) y = 35, find x when constant of variation = 7.

#### Question 1:

Explain the concept of direct variation.

#### Question 2:

Which of the following quantities vary directly with each other?
(i) Number of articles (x) and their price (y).
(ii) Weight of articles (x) and their cost (y).
(iii) Distance x and time y, speed remaining the same.
(iv) Wages (y) and number of hours (x) of work.
(v) Speed (x) and time (y) (distance covered remaining the same).
(vi) Area of a land (x) and its cost (y).

(i) The number of articles is directly related to the price. Therefore, they will vary directly with each other.
(ii) The number of articles is directly related to the weight of the articles. Therefore, they will vary directly with each other.
(iii) Speed is constant. Therefore, distance and time does not vary directly.
(iv) The number of hours is directly related to the wages. Therefore, it is a direct variation.
(v) Distance is constant. Therefore, speed and time does not vary directly.
(vi) If the area of a land is large, its cost will also be high. Thus, it is a direct variation.

Thus, the respective values in (i), (ii), (iv) and (vi) vary directly with each other.

#### Question 3:

In which of the following tables x and y vary directly?
(i)

 a 7 9 13 21 25 b 21 27 39 63 75

(ii)
 a 10 20 30 40 46 b 5 10 15 20 23

(iii)
 a 2 3 4 5 6 b 6 9 12 17 20

(iv)
 a 12 22 32 42 52 b 13 23 33 43 53

#### Question 4:

Fill in the blanks in each of the following so as to make the statement true:
(i) Two quantities are said to vary.... with each other if they increase (decrease) together in such a way that the ratio of the corresponding values remains same.
(ii) x and y are said to vary directly with each other if for some positive number k,...... = k.
(iii) If u = 3 v, then u and v vary .... with each other.

#### Question 5:

Complite the following tables given that x varies directly as y.
(i)

 x 2.5 ... ... 15 y 5 8 12 ...

(ii)
 x 5 ... 10 35 25 ... y 8 12 ... ... ... 32

(iii)
 x 6 8 10 ... 20 y 15 20 ... 40 ...

(iv)
 x 4 9 ... ... 3 ... y 16 ... 48 36 ... 4

(v)
 x 3 5 7 9 y ... 20 28 ...

#### Question 6:

Find the constant of variation from the table given below:

 x 3 5 7 9 y 12 20 28 36
Set up a table and solve the following problems. Use unitary method to verify the answer.

#### Question 7:

Rohit bought 12 registers for Rs 156, find the cost of 7 such registers.

Let the cost of 7 registers beâ€‹ Rs x.

 Register 12 7 Cost(in Rs.) 156 x

#### Question 8:

Anupama takes 125 minutes in walking a distance of 100 metre. What distance would she cover in 315 minutes?

Let the distance travelled in 315 minutes be x km.

 Time (in minute) 125 315 Distance(in metre) 100 x

#### Question 9:

If the cost of 93 m of a certain kind of plastic sheet is Rs 1395, then what would it cost to buy 105 m of such plastic sheet?

 Length of plastic sheet (in metre) 93 105 Cost (in Rs) 1395 x

Let the cost of the plastic sheet per metre be Rs x.

#### Question 10:

Suneeta types 1080 words in one hour. What is her GWAM (gross words a minute rate)?

 Number of words 1080 x Time (in minute) 60 1

Let x be her GWAM.

#### Question 11:

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

 Distance (in km) 50 x Time (in minute) 60 12

Let the distance be x km.

#### Question 12:

68 boxes of a certain commodity require a shelf-length of 13.6 m. How many boxes of the same commodity would occupy a shelf length of 20.4 m?

 Number of Boxes 68 x Shelf-length (in m) 13.6 20.4

Let x be the number of boxes that occupy a shelf-length of 20.4 m.

#### Question 13:

In a library 136 copies of a certain book require a shelf-length of 3.4 metre. How many copies of the same book would occupy a shelf-length of 5.1 metres?

 Number of copies 136 x Length the shelf (in m) 3.4 5.1

Let x be the number of copies that would occupy a shelf-length of 5.1 m.

#### Question 14:

The second class railway fare for 240 km of Journey is Rs 15.00. What would be the fare for a journey of 139.2 km?

Let Rs x be the fare for a journey of 139.2 km.

 Distance (in km) 240 139.2 Fare (in Rs.) 15 x

#### Question 15:

If the thickness of a pile of 12 cardboards is 35 mm, find the thickness of a pile of 294 cardboards.

Let x cm be the thickness of a pile of 294 cardboards.

 Thickness (in cm) 3.5 x Cardboard 12 294

#### Question 16:

The cost of 97 metre of cloth is Rs 242.50. What length of this can be purchased for Rs 302.50?

Let x metre be the length of the cloth that can be purchased for Rs 302.50.

 Length (in m) 97 x Cost (in Rs) 242.5 302.50

#### Question 17:

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 number of men required to dig a trench of 27 metre.

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

#### Question 18:

A worker is paid Rs 210 for 6 days work. If his total income of the month is Rs 875, for how many days did he work?

Let x be the number of days for which the worker is paid Rs 875.

 Income (in Rs.) 210 875 Number of days 6 x

#### Question 19:

A woker is paid Rs 200 for 8 days work. If he works for 20 days, how much will he get?

Let Rs x be the income for 20 days of work.

 Income (in Rs) 200 x Number of days 8 20

#### Question 20:

The amount of extension in an elastic string varies directly as the weight hung on it. If a weight of 150 gm produces an extension of 2.9 cm, then what weight would produce an extension of 17.4 cm?

Let x gm be the weight that would produce an extension of 17.4 cm.

 Weight (in gm) 150 x Length (in cm) 2.9 17.4

#### Question 21:

The amount of extension in an elastic spring varies directly with the weight hung on it. If a weight of 250 gm produces an extension of 3.5 cm, find the extension produced by the weight of 700 gm.

Let x cm be the extension produced by the weight of 700 gm.

 Weight (in gm) 250 700 Length (in cm) 3.5 x

#### Question 22:

In 10 days, the earth picks up 2.6 × 108 pounds of dust from the atmosphere. How much dust will it pick up in 45 days?

Let the amount of dust picked up by the earth in 45 days be x pounds.

#### Question 23:

In 15 days, the earth picks up 1.2 × 108 kg of dust from the atmosphere. In how many days it will pick up 4.8 × 108 kg of dust?

Let x be the number of days taken by the earth to pick up $4.8×{10}^{8}$ kg of dust.