RD Sharma solution class 7 chapter 10 Unitary Method Exercise 10.1

Exercise 10.1

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Question 1:

20 chocolates cost Rs 320. Find the cost of 35 such chocolates.

Answer 1:

Cost of 20 chocolates  = Rs. 320
Cost of 1 chocolate    =  Rs. 320 ÷ 20 =  16
So, cost of 35 chocolates = 35  ×  16 = Rs. 560

Question 2:

The cost of 40 metres of cloth is Rs 200. Find the cost of 50 metres of cloth.

Answer 2:

Cost of 40 metres of cloth = Rs. 200
Therefore, cost of 1 metre of cloth = Rs. $200÷40 = \mathrm{Rs}. 5$
Hence, cost of 50 metres of cloth = Rs. 5(50) = Rs. 250

Question 3:

A car can cover a distance of 522 km on 36 litres of petrol. How far can it travel on 14 litres of petrol?

Answer 3:

Distance covered by the car on 36 litres  = 522 km
Distance covered by the car on 1 litre = 522 ÷ 36
Distance covered by the car on 14 litres = (522 ÷ 36) × 14  = 203 km 

Question 4:

Travelling 900 km by rail costs Rs 280. What would be the fare for a journey of 360 km when a person travels by the same class?

Answer 4:

Fare for 900 km of rail travel = Rs. 280
Fare for 1 km =  Rs. 280 ÷  900
Therefore, fare for 360 km = (280 ÷ 900) × 360 =  Rs. 112

Question 5:

If 6 oil tankers can be filled by a pipe in 4 $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ hours, how long does the pipe take to fill 4 such oil tankers?

Answer 5:

Time taken by the pipe to fill 6 oil tankers = 4 1/2 = 9/2 hours
Time taken to fill 1 oil tanker =  $\frac{9}{2}\times \frac{1}{6} = \frac{3}{4}\mathrm{hours}$
Therefore, the pipe will be able to fill 4 oil tankers in $\frac{3}{4}\times 4 = 3 \mathrm{hours}.$

Question 6:

3/4 of the salary per month is Rs 600. What is the salary per month?

Answer 6:

Let the salary be Rs. x.
Then, 3/4 of the salary per month = Rs. 600.
That is, (3/4) x = 600
⇒ x = (4​ × 600) ÷ 3 = Rs. 800
So, the salary = Rs. 800.

Question 7:

The cost of 32 tables is Rs 23520. Find the number of such tables that can be purchased for Rs 51450.

Answer 7:

With Rs. 23520, we can buy 32 tables.
Therefore, with Re. 1, we can buy $\frac{32}{23520}$ tables.
Hence, the number of tables that we can purchase with Rs. 51450 = $\frac{2}{23520}\times 51450$ = 70.

Question 8:

The yield of wheat from 6 hectares is 280 quintals. Find the number of hectares required for a yield of 225 quntals.

Answer 8:

Yield of wheat from 6 hectares = 280 quintals
Yield of wheat from 1 hectare = 280 ÷ 6 =  46.66 quintals
Number of hectares required for a yield of 225 quintals = 225 ÷ 46.66 = 4.8 hectares
So, 4.8 hectares is required for a yield of 225 quintals.

Question 9:

Fifteen post cards cost Rs 2.25. What will be the cost of 36 post cards? How many postcards can we buy in Rs 45?

Answer 9:

Cost of 15 postcards = Rs. 2.25
Cost of 1 postcard = Rs. 2.25 ​÷ 15  =  Rs. 0.15
Cost of 36 postcards = 36 × (2.25 ÷ 15) =  Rs. 5.4
Number of postcards that can be bought for Rs. 45 = 45 ​÷ 0.15 = 300

Question 10:

A rail journey of 75 km costs Rs 215. How much will a journey of 120 km cost?

Answer 10:

Fare for a rail journey of 75 km = Rs. 215
Fare for 1 km = Rs. 215 ÷ 75 =  Rs. 2.86
Fare for 120 km = Rs. 120  × 2.86 = Rs. 343.2

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Question 11:

If the sales tax on a purchase wirth Rs 60 is Rs 4.20. What will be the sales tax on the purchase worth of Rs 150?

Answer 11:

Sales tax on purchase worth Rs. 60 = Rs. 4.20
Sales tax on purchase worth Re. 1 = 4.20 ÷  60
Therefore, sales tax on purchase worth Rs. 150 = Rs. 150 × (4.20 ÷ 60) = Rs. 10.5.

Question 12:

52 packets of 12 pencils each, cost Rs 499.20. Find the cost of 65 packets of 10 pencils each.

Answer 12:

Cost of 52 packets of 12 pencils each = Rs. 499.20
Cost of 1 packet of 12 pencils = Rs. 499.20 ​÷ 52 = Rs. 9.6
Therefore, cost of 12 pencils = Rs. 9.6
So, cost of 1 pencil = Rs. 9.6 ÷ 12 = Rs. 0.8
Cost of 10 pencils = Rs. 10 × (9.6 ​÷ 12) = Rs. 8
Therefore, cost of 1 packet of 10 pencils each = Rs. 8
Hence, cost of 65 packets of 10 pencils each =  65  × Rs. 8 = Rs. 520