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Chapter 10: Unitary Method Exercise – 10.1 Question: 1 20 chocolates cost Rs 320. Find the cost of 35 such chocolates. Solution: Cost of 20 chocolates = Rs 320 Cost of 1 chocolate = Rs (320/20) Therefore, the cost of 35 chocolates = Rs ((320/20) × 35) = Rs 560 Question: 2 The cost of 40 meters of cloth is Rs 200. Find the cost of 50 meters of cloth. Solution: Cost of 40 meters of cloth = Rs 200 Cost of 1 meter of cloth = Rs (200/40) Therefore, the cost of 50 chocolates = Rs ((200/40) × 50) = Rs 250 Question: 3 A car can cover a distance of 522 km on 36 liters of petrol. How far can it travel on 14 litres of petrol? Solution: Number of kilometers a car can cover by using 36 liters = 522 km Number of kilometers a car can cover by using 1 liter = 522/36 km Hence, the number of kilometers a car can cover by using 14 liters = ((522/36) × 14) km = 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? Solution: Cost of travelling 900 km by rail = Rs 280 Cost of travelling 1 km by rail = Rs (280/900) Hence, Cost of travelling 360 km by rail = Rs (280/900) × 360 = Rs 112 Question: 5 If 6 oil tankers can be filled by a pipe in 4(1/2) hours, how long does the pipe take to fill 4 such oil tankers? Solution: Question: 6 3/4 of the salary per month is Rs 600. What is the salary per month? Solution: Question: 7 The cost of 32 tables is Rs 23520. Find the number of such tables that can be purchased for Rs 51450. Solution: Number of tables bought for Rs 23520 = 32 Number of tables bought for Re 1 = 32/23520 Number of tables bought for Rs 51450 = (32/23520) × 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 quintals. Solution: Number of hectares required for a yield of 280 quintals = 6 hectares Number of hectares required for a yield of 1 quintal = 6/280 hectares Hence, the number of hectares required for a yield of 225 quintals = 6/280 × 225 hectares = 4(23/28) hectares 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? Solution: Question: 10 A rail journey of 75 km costs Rs 215. How much will a journey of 120 km cost? Solution: Cost of a rail journey of 75 km = Rs 215 Cost of a rail journey of 1 km = Rs 215/75 Cost of a rail journey of 120 km = Rs 215/75 × 120 = Rs 344 Question: 11 If the sales tax on a purchase worth Rs 60 is Rs 4.20. What will be the sales tax on the purchase worth of Rs 150? Solution: Sales tax on the purchase worth of Rs 60 = Rs 4.20 Sales tax on the purchase worth of Re 1 = Rs 4.2060 Sales tax on the purchase worth of Rs 150 = Rs (4.20/60) × 150 = Rs 10.50 Question: 12 52 packets of 12 pencils each, cost Rs 499.20. Find the cost of 65 packets of 10 pencils each. Solution: Total number of pencils in 52 packets of 12 pencils each = 52 × 12 = 624 Cost of 624 pencils = Rs 499.20 Cost of 1 pencil = Rs 499.20/624 Now, Number of pencils in 65 packets of 10 pencils each = 65 x 10 = 650 pencils Therefore, cost of 650 pencils = Rs (499.20/624) × 650 = Rs 520.
20 chocolates cost Rs 320. Find the cost of 35 such chocolates.
Cost of 20 chocolates = Rs 320
Cost of 1 chocolate = Rs (320/20)
Therefore, the cost of 35 chocolates = Rs ((320/20) × 35) = Rs 560
The cost of 40 meters of cloth is Rs 200. Find the cost of 50 meters of cloth.
Cost of 40 meters of cloth = Rs 200
Cost of 1 meter of cloth = Rs (200/40)
Therefore, the cost of 50 chocolates = Rs ((200/40) × 50) = Rs 250
A car can cover a distance of 522 km on 36 liters of petrol. How far can it travel on 14 litres of petrol?
Number of kilometers a car can cover by using 36 liters = 522 km
Number of kilometers a car can cover by using 1 liter = 522/36 km
Hence, the number of kilometers a car can cover by using 14 liters = ((522/36) × 14) km = 203 km
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?
Cost of travelling 900 km by rail = Rs 280
Cost of travelling 1 km by rail = Rs (280/900)
Hence, Cost of travelling 360 km by rail = Rs (280/900) × 360 = Rs 112
If 6 oil tankers can be filled by a pipe in 4(1/2) hours, how long does the pipe take to fill 4 such oil tankers?
3/4 of the salary per month is Rs 600. What is the salary per month?
The cost of 32 tables is Rs 23520. Find the number of such tables that can be purchased for Rs 51450.
Number of tables bought for Rs 23520 = 32
Number of tables bought for Re 1 = 32/23520
Number of tables bought for Rs 51450 = (32/23520) × 51450 = 70
The yield of wheat from 6 hectares is 280 quintals. Find the number of hectares required for a yield of 225 quintals.
Number of hectares required for a yield of 280 quintals = 6 hectares
Number of hectares required for a yield of 1 quintal = 6/280 hectares
Hence, the number of hectares required for a yield of 225 quintals = 6/280 × 225 hectares = 4(23/28) hectares
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?
A rail journey of 75 km costs Rs 215. How much will a journey of 120 km cost?
Cost of a rail journey of 75 km = Rs 215
Cost of a rail journey of 1 km = Rs 215/75
Cost of a rail journey of 120 km = Rs 215/75 × 120 = Rs 344
If the sales tax on a purchase worth Rs 60 is Rs 4.20. What will be the sales tax on the purchase worth of Rs 150?
Sales tax on the purchase worth of Rs 60 = Rs 4.20
Sales tax on the purchase worth of Re 1 = Rs 4.2060
Sales tax on the purchase worth of Rs 150 = Rs (4.20/60) × 150 = Rs 10.50
52 packets of 12 pencils each, cost Rs 499.20. Find the cost of 65 packets of 10 pencils each.
Total number of pencils in 52 packets of 12 pencils each = 52 × 12 = 624
Cost of 624 pencils = Rs 499.20
Cost of 1 pencil = Rs 499.20/624
Now,
Number of pencils in 65 packets of 10 pencils each = 65 x 10 = 650 pencils
Therefore, cost of 650 pencils = Rs (499.20/624) × 650 = Rs 520.
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