# Worksheet on ratio and proportion word problem

In this post, students will get Word problem worksheet based on the ratio and proportion with the solution. So, if you are looking for word problems, read this post completely.

Q.1 The ratio of the number of boys and girls in a school of 720 students is 7: 5 . How many more girls should be admitted to make the ratio 1: 1?

Q.2 The income of A and B are in the ratio 3:2 and their expenditures in the ratio 5:3. If each saves 1500 Rs, find the income of B

Q.3 The ratio of a father’s age that of his son is 3:1. If the sum of their ages is 60, find their ages

Q.4 Anil purchases 10 notebooks for 150 Rs and Neeraj buys 8 notebooks for 96 Rs. Who got the notebooks at a lesser cost?

Q.5 In an examination,91% of the candidates passed and 18 failed. How many candidates appeared in the examination.

Q.6 The angles of a triangle are in the ratio 1: 2: 3.Find the angles of the triangle

Q.7 In an examination, a student must get 40 % marks to pass. Another student who gets 250 marks, fails by 14 marks. Find the maximum marks

Q.8 Three players scored 250 runs in a one-day cricket match in the ratio 2:3:5.Find the score of each player.

Solution:

Problem: 01

The ratio of the number of boys and girls in a school of 720 students is 7: 5 . How many more girls should be admitted to make the ratio 1: 1?

Solution:

Total number of students in the school = 720

No . of boys and girls are in the ratio = 7: 5

Let the No . of boys and girls in the school are 7x and 5x respectively

Problem: 02

The income of A and B are in the ratio 3:2 and their expenditures in the ratio 5:3. If each saves 1500 Rs, find the income of B

Solution :

Let the income of A and B are 3x and 2x respectively while their expenditures are 5y and 3y

Amount of income both saves = 1500 Rs

We know,

Saving = Income  – Expenditure

∴ Saving of A’s

3x – 5y = 1500        ……..(i)

And, Saving of B’s

2x – 3y = 1500        ………(ii)

Solving eq(i) and (ii), we get

x = 3000 and y = 1500

Hence , B’s income = 2x = 2×3000 = 6000 Rs

Problem: 03

The ratio of a father’s age that of his son is 3:1. If the sum of their ages is 60, find their ages

Solution:

Let the age of the father and his son is 3x and x respectively

Since the sum of their ages is 60

∴  3x + x = 60

4x = 60

x = 15

Hence ,

Son’s age = 15 years

His father age = 3× x = 3× 15 = 45 years

Problem : 04

Anil purchases 10 notebooks for 150 Rs and Neeraj buys 8 notebooks for 96 Rs. Who got the notebooks at a lesser cost?

Solution:

Anil purchases 10 notebooks for 150 Rs

So, price of 1 notebook   = \frac{150}{10} = 15 Rs

Similarly

Neeraj purchases 8 notebooks for 96 Rs

So, price of 1 notebook = \frac{96}{8}

= 12 Rs

Hence, Neeraj got notebooks at a lesser cost than Anil

Problem: 05

In an examination,91% of the candidates passed and 18 failed. How many candidates appeared in the examination.

Solution:

Let the no. of candidates who appeared in the examination are x

Since 91 % of the candidates passed the exam. That means 9 % of candidates failed the exam

No . of failed candidates = 18

∴ 9 % of x = 18

\frac{9}{100} x = 18

9x = 1800

x = 200

So, the total no . of candidates who appeared in the exam are 200

Problem: 06

The angles of a triangle are in the ratio 1: 2: 3.Find the angles of the triangle

Solution:

Let the angles of the triangle are x, 2x, and 3x.

We know, Sum of all angles of the triangle = 180º

∴ x + 2x +3x = 180

6x = 180

x = 30º

Hence, Angles of triangle are

x = 30º .2x= 2×30=60º and 3x=3×30=90º

Problem: 07

In an examination, a student must get 40 % marks to pass. Another student who gets 250 marks, fails by 14 marks. Find the maximum marks

Solution:

Let the maximum marks in the examination is x

No . of marks required to pass the examination = 40 % of x     ……..(i)

A student who got 250 marks but fail by 14 marks ,that means minimum passing mark = 250 + 14 = 264 …(ii)

From eq(i) and (ii)

40 % of x = 264

\frac{40}{100} of x = 264

\frac{4}{10} of x = 264

\frac{4x}{10} = 264

4x = 264 × 10

4x = 2640

x = 660 marks

Hence , Maximum marks in the examination is 660 marks

Problem: 08

Three players scored 250 runs in a one-day cricket match in the ratio 2:3:5.Find the score of each player.

Solution:

Let the run scored by three players(P1 ,P2 and P3)  are 2x , 3x and 5x respectively .

Total run scored by these three players = 250 Runs

∴  2x + 3x + 5x = 250

10x = 250

x = 25

Hence ,

P1 = 2x = 2×25= 50 runs

P2 = 3x= 3×25= 75 runs

P3 = 5x = 5×25= 125 runs

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