In this post, students will ge**t 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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