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Unitary Method RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

Q: 4. What are the key steps involved in solving a unitary method problem?

Ans. The key steps in solving a unitary method problem are:1. Identify the known and unknown quantities.2. Determine whether the problem involves direct or inverse proportion.3. Set up a proportion equation using the given values.4. Solve the proportion equation to find the unknown quantity.

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 Page 1


 
 
 
 
 
 
 
 
Exercise 10.1        Page No: 10.2 
 
1. 20 chocolates cost Rs 320. Find the cost of 35 such chocolates. 
 
Solution: 
Given cost of 20 chocolates = Rs 320 
Cost of 1 chocolate = (320/20) 
Therefore, the cost of 35 chocolates = (320/20) × 35  
= Rs 560 
 
2. The cost of 40 meters of cloth is Rs 200. Find the cost of 50 meters of cloth. 
 
Solution: 
Given cost of 40 meters of cloth = Rs 200 
Cost of 1 meter of cloth = (200/40) 
Therefore, the cost of 50 chocolates = (200/40) × 50  
= Rs 250 
 
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? 
 
Solution: 
Given that number of kilometres a car can cover by using 36 litres of petrol = 522 km 
Number of kilometres a car can cover by using 1 litre of petrol = 522/36 
Hence, the number of kilometres a car can cover by using 14 litres = (522/36) × 14  
= 203 km 
 
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: 
Given that cost of travelling 900 km by rail = Rs 280 
Therefore cost of travelling 1 km by rail = (280/900) 
Hence, Cost of travelling 360 km by rail = (280/900) × 360  
= Rs 112 
 
Page 2


 
 
 
 
 
 
 
 
Exercise 10.1        Page No: 10.2 
 
1. 20 chocolates cost Rs 320. Find the cost of 35 such chocolates. 
 
Solution: 
Given cost of 20 chocolates = Rs 320 
Cost of 1 chocolate = (320/20) 
Therefore, the cost of 35 chocolates = (320/20) × 35  
= Rs 560 
 
2. The cost of 40 meters of cloth is Rs 200. Find the cost of 50 meters of cloth. 
 
Solution: 
Given cost of 40 meters of cloth = Rs 200 
Cost of 1 meter of cloth = (200/40) 
Therefore, the cost of 50 chocolates = (200/40) × 50  
= Rs 250 
 
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? 
 
Solution: 
Given that number of kilometres a car can cover by using 36 litres of petrol = 522 km 
Number of kilometres a car can cover by using 1 litre of petrol = 522/36 
Hence, the number of kilometres a car can cover by using 14 litres = (522/36) × 14  
= 203 km 
 
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: 
Given that cost of travelling 900 km by rail = Rs 280 
Therefore cost of travelling 1 km by rail = (280/900) 
Hence, Cost of travelling 360 km by rail = (280/900) × 360  
= Rs 112 
 
 
 
 
 
 
 
 
 
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: 
Given that time taken by 6 oil tankers to be filled by a pipe = 4 (1/2) hours = (9/2) hours 
Time taken by 1 oil tanker to be filled by a pipe = (9/2)/6 hours = 9/ (2 x 6) = 9/12 hours 
Hence time taken by 4 oil tankers to be filled by a pipe = (9/12) × 4 
= 3 hours 
 
6. 3/4 of the salary per month is Rs 600. What is the salary per month? 
 
Solution: 
Given that 3/4 of the salary per month = 600 
Let the salary of the month be x 
Therefore ¾ × x = 600 
x = 600 × (4/3) 
x = 800 
Therefore salary per month is Rs 800 
 
7.  The cost of 32 tables is Rs 23520. Find the number of such tables that can be 
purchased for Rs 51450. 
 
Solution: 
Given that number of tables bought for Rs 23520 = 32 
Number of tables bought for Rs 1 = 32/23520 
Hence, number of tables bought for Rs 51450 = (32/23520) × 51450 = 70 
 
8. The yield of wheat from 6 hectares is 280 quintals. Find the number of hectares 
required for a yield of 225 quintals. 
 
Solution: 
Given 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 
= 4 23/28 hectares 
 
9. Fifteen post cards cost Rs 2.25. What will be the cost of 36 post cards? How many 
Page 3


 
 
 
 
 
 
 
 
Exercise 10.1        Page No: 10.2 
 
1. 20 chocolates cost Rs 320. Find the cost of 35 such chocolates. 
 
Solution: 
Given cost of 20 chocolates = Rs 320 
Cost of 1 chocolate = (320/20) 
Therefore, the cost of 35 chocolates = (320/20) × 35  
= Rs 560 
 
2. The cost of 40 meters of cloth is Rs 200. Find the cost of 50 meters of cloth. 
 
Solution: 
Given cost of 40 meters of cloth = Rs 200 
Cost of 1 meter of cloth = (200/40) 
Therefore, the cost of 50 chocolates = (200/40) × 50  
= Rs 250 
 
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? 
 
Solution: 
Given that number of kilometres a car can cover by using 36 litres of petrol = 522 km 
Number of kilometres a car can cover by using 1 litre of petrol = 522/36 
Hence, the number of kilometres a car can cover by using 14 litres = (522/36) × 14  
= 203 km 
 
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: 
Given that cost of travelling 900 km by rail = Rs 280 
Therefore cost of travelling 1 km by rail = (280/900) 
Hence, Cost of travelling 360 km by rail = (280/900) × 360  
= Rs 112 
 
 
 
 
 
 
 
 
 
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: 
Given that time taken by 6 oil tankers to be filled by a pipe = 4 (1/2) hours = (9/2) hours 
Time taken by 1 oil tanker to be filled by a pipe = (9/2)/6 hours = 9/ (2 x 6) = 9/12 hours 
Hence time taken by 4 oil tankers to be filled by a pipe = (9/12) × 4 
= 3 hours 
 
6. 3/4 of the salary per month is Rs 600. What is the salary per month? 
 
Solution: 
Given that 3/4 of the salary per month = 600 
Let the salary of the month be x 
Therefore ¾ × x = 600 
x = 600 × (4/3) 
x = 800 
Therefore salary per month is Rs 800 
 
7.  The cost of 32 tables is Rs 23520. Find the number of such tables that can be 
purchased for Rs 51450. 
 
Solution: 
Given that number of tables bought for Rs 23520 = 32 
Number of tables bought for Rs 1 = 32/23520 
Hence, number of tables bought for Rs 51450 = (32/23520) × 51450 = 70 
 
8. The yield of wheat from 6 hectares is 280 quintals. Find the number of hectares 
required for a yield of 225 quintals. 
 
Solution: 
Given 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 
= 4 23/28 hectares 
 
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: 
Given cost of 15 post cards = Rs 2.25 
Cost of 1 post card is = 2.25/15 
Hence, the cost of 36 post cards = (2.25/15) × 36 
= Rs 5.40 
Number of post cards bought for Rs 2.25 = 15 
Numbers of post cards bought for Rs 1 = 15/2.25 
Hence number of post cards bought for Rs 45 = (15/2.25) × 45 
= 300 
 
10. A rail journey of 75 km costs Rs 215. How much will a journey of 120 km cost? 
 
Solution: 
Given cost of a rail journey of 75 km = Rs 215 
Cost of a rail journey of 1 km = 215/75 
Hence, cost of a rail journey of 120 km = (215/75) × 120  
= Rs 344 
 
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: 
Given sales tax on the purchase worth of Rs 60 = Rs 4.20 
Sales tax on the purchase worth of Rs 1 = Rs 4.2060 
Hence, sales tax on the purchase worth of Rs 150 = (4.20/60) × 150  
= Rs 10.50 
 
12. 52 packets of 12 pencils each, cost Rs 499.20. Find the cost of 65 packets of 10 
pencils each. 
 
Solution: 
Given total number of pencils in 52 packets of 12 pencils each = 52 × 12  
= 624 pencils 
Also given that cost of 624 pencils = Rs 499.20 
Cost of 1 pencil = (499.20/624) 
Page 4


 
 
 
 
 
 
 
 
Exercise 10.1        Page No: 10.2 
 
1. 20 chocolates cost Rs 320. Find the cost of 35 such chocolates. 
 
Solution: 
Given cost of 20 chocolates = Rs 320 
Cost of 1 chocolate = (320/20) 
Therefore, the cost of 35 chocolates = (320/20) × 35  
= Rs 560 
 
2. The cost of 40 meters of cloth is Rs 200. Find the cost of 50 meters of cloth. 
 
Solution: 
Given cost of 40 meters of cloth = Rs 200 
Cost of 1 meter of cloth = (200/40) 
Therefore, the cost of 50 chocolates = (200/40) × 50  
= Rs 250 
 
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? 
 
Solution: 
Given that number of kilometres a car can cover by using 36 litres of petrol = 522 km 
Number of kilometres a car can cover by using 1 litre of petrol = 522/36 
Hence, the number of kilometres a car can cover by using 14 litres = (522/36) × 14  
= 203 km 
 
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: 
Given that cost of travelling 900 km by rail = Rs 280 
Therefore cost of travelling 1 km by rail = (280/900) 
Hence, Cost of travelling 360 km by rail = (280/900) × 360  
= Rs 112 
 
 
 
 
 
 
 
 
 
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: 
Given that time taken by 6 oil tankers to be filled by a pipe = 4 (1/2) hours = (9/2) hours 
Time taken by 1 oil tanker to be filled by a pipe = (9/2)/6 hours = 9/ (2 x 6) = 9/12 hours 
Hence time taken by 4 oil tankers to be filled by a pipe = (9/12) × 4 
= 3 hours 
 
6. 3/4 of the salary per month is Rs 600. What is the salary per month? 
 
Solution: 
Given that 3/4 of the salary per month = 600 
Let the salary of the month be x 
Therefore ¾ × x = 600 
x = 600 × (4/3) 
x = 800 
Therefore salary per month is Rs 800 
 
7.  The cost of 32 tables is Rs 23520. Find the number of such tables that can be 
purchased for Rs 51450. 
 
Solution: 
Given that number of tables bought for Rs 23520 = 32 
Number of tables bought for Rs 1 = 32/23520 
Hence, number of tables bought for Rs 51450 = (32/23520) × 51450 = 70 
 
8. The yield of wheat from 6 hectares is 280 quintals. Find the number of hectares 
required for a yield of 225 quintals. 
 
Solution: 
Given 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 
= 4 23/28 hectares 
 
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: 
Given cost of 15 post cards = Rs 2.25 
Cost of 1 post card is = 2.25/15 
Hence, the cost of 36 post cards = (2.25/15) × 36 
= Rs 5.40 
Number of post cards bought for Rs 2.25 = 15 
Numbers of post cards bought for Rs 1 = 15/2.25 
Hence number of post cards bought for Rs 45 = (15/2.25) × 45 
= 300 
 
10. A rail journey of 75 km costs Rs 215. How much will a journey of 120 km cost? 
 
Solution: 
Given cost of a rail journey of 75 km = Rs 215 
Cost of a rail journey of 1 km = 215/75 
Hence, cost of a rail journey of 120 km = (215/75) × 120  
= Rs 344 
 
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: 
Given sales tax on the purchase worth of Rs 60 = Rs 4.20 
Sales tax on the purchase worth of Rs 1 = Rs 4.2060 
Hence, sales tax on the purchase worth of Rs 150 = (4.20/60) × 150  
= Rs 10.50 
 
12. 52 packets of 12 pencils each, cost Rs 499.20. Find the cost of 65 packets of 10 
pencils each. 
 
Solution: 
Given total number of pencils in 52 packets of 12 pencils each = 52 × 12  
= 624 pencils 
Also given that cost of 624 pencils = Rs 499.20 
Cost of 1 pencil = (499.20/624) 
 
 
 
 
 
 
 
 
Number of pencils in 65 packets of 10 pencils each = 65 x 10  
= 650 pencils 
Therefore, cost of 650 pencils = (499.20/624) × 650  
= Rs 520.

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FAQs on Unitary Method RD Sharma Solutions - Mathematics (Maths) Class 7

1. What is the unitary method in mathematics?

Ans. The unitary method is a mathematical technique used to solve problems involving direct or inverse proportion. It allows us to find the value of one variable when the values of other variables are known.

2. How can the unitary method be applied to solve real-life problems?

Ans. The unitary method can be applied to solve real-life problems by establishing a direct or inverse relationship between two or more quantities and using this relationship to find the unknown quantity. For example, it can be used to calculate the cost of a certain number of items given the cost of a single item.

3. Can you provide an example of how the unitary method is used in daily life?

Ans. Sure! Let's say a recipe requires 2 cups of flour to make 12 cookies. If you want to make 24 cookies, you can use the unitary method to find out how much flour you will need. Since the number of cookies has doubled, the amount of flour needed will also double, so you will need 4 cups of flour.

4. What are the key steps involved in solving a unitary method problem?

Ans. The key steps in solving a unitary method problem are: 1. Identify the known and unknown quantities. 2. Determine whether the problem involves direct or inverse proportion. 3. Set up a proportion equation using the given values. 4. Solve the proportion equation to find the unknown quantity.

5. Are there any shortcuts or tricks to solve unitary method problems quickly?

Ans. Yes, there are a few tricks that can help solve unitary method problems more quickly. One such trick is cross-multiplication, where you multiply the extremes (the product of the first and last terms) and the means (the product of the second and third terms) of a proportion equation to solve for the unknown quantity. Another trick is to use ratios to compare different quantities and simplify the problem.

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