Ratio word problems help us apply ratio concepts to real-life situations such as ages, money distribution, expenditure, marks, population, and other practical scenarios.
This section covers important ratio word problems with step-by-step solutions that are frequently asked in SSC, RRB, Banking, Defence, NDA, CDS, school examinations, and other competitive exams.
If you are new to this topic, we recommend first reading our Ratio and Proportion section to understand the basic concepts.
To learn the important formulas used to solve these questions quickly, you can also check our Ratio Formula with Examples and Explanations page.
By solving the questions given below, you will develop a strong understanding of how ratio concepts are applied in real-life situations and competitive examinations.
Question 1:
The teacher is 42 years old and her student is 14 years old.
Find:
(a) The ratio of the teacher’s age to the student’s age at present.
(b) The ratio of their ages when the student was 10 years old.
(c) The ratio of their ages after 8 years.
(d) The ratio of their ages when the teacher was 30 years old.
Solution:
Teacher’s Present Age = 42 years
Student’s Present Age = 14 years
(a) Ratio of the teacher’s age to the student’s age at present
Teacher : Student
= 42 : 14 (HCF of 42 & 14 is 14)
= (42/14) : (14/14)
= 3 : 1
Answer: 3 : 1
(b) Ratio of their ages when the student was 10 years old
The student is currently 14 years old.
Years ago when the student was 10 years old
= 14 − 10
= 4 years ago
Teacher’s age 4 years ago
= 42 − 4
= 38 years
Student’s age 4 years ago
= 10 years
Ratio
= 38 : 10
= 19 : 5
Answer: 19 : 5
(c) Ratio of their ages after 8 years
Teacher’s age after 8 years
= 42 + 8
= 50 years
Student’s age after 8 years
= 14 + 8
= 22 years
Ratio
= 50 : 22
= 25 : 11
Answer: 25 : 11
(d) Ratio of their ages when the teacher was 30 years old
Teacher’s present age = 42 years
Years ago when the teacher was 30 years old
= 42 − 30
= 12 years ago
Student’s age 12 years ago
= 14 − 12
= 2 years
Ratio
= 30 : 2
= 15 : 1
Answer: 15 : 1
Question 2:
Two SSC aspirants, Rohit and Aman, jointly purchased 25 mock test papers for ₹500.
Rohit contributed ₹200, while Aman contributed ₹300.
After purchasing the mock tests, Rohit suggested that both should receive an equal number of papers, i.e., 12.5 papers each.
Aman disagreed and said that the papers should be divided according to the amount contributed by each person.
Who is correct? How many mock test papers should each student receive?
Solution
Amount contributed by Rohit = ₹200
Amount contributed by Aman = ₹300
Ratio of Contributions
= 200 : 300
= 2 : 3
Since the mock test papers must be divided according to the amount contributed, we use the Formula to Divide a Quantity in a Given Ratio.
If a quantity Q is divided in the ratio A : B, then
First Share
= [A/(A + B)] × Q
Second Share
= [B/(A + B)] × Q
Here,
Q = 25 mock test papers
A : B = 2 : 3
Rohit’s Share
= [2/(2 + 3)] × 25
= (2/5) × 25
= 10
Aman’s Share
= [3/(2 + 3)] × 25
= (3/5) × 25
= 15
Therefore,
Rohit should receive 10 mock test papers and Aman should receive 15 mock test papers.
Since Rohit and Aman did not contribute equal amounts, the papers should not be divided equally.
Hence, Aman is correct.
Question 3:
A mother wants to distribute ₹360 between her daughters, Shreya and Bhoomika, in the ratio of their ages. If Shreya is 15 years old and Bhoomika is 12 years old, find the amount received by each daughter.
Solution
Age of Shreya = 15 years
Age of Bhoomika = 12 years
Ratio of their ages
= 15 : 12
= (15/3) : (12/3)
= 5 : 4
Since the money is to be distributed in the ratio of their ages, we use the Formula to Divide a Quantity in a Given Ratio.
If a quantity Q is divided in the ratio A : B, then
First Share
= [A/(A + B)] × Q
Second Share
= [B/(A + B)] × Q
Here,
Q = ₹360
A : B = 5 : 4
Shreya’s Share
= [5/(5 + 4)] × 360
= (5/9) × 360
= ₹200
Bhoomika’s Share
= [4/(5 + 4)] × 360
= (4/9) × 360
= ₹160
Therefore,
Shreya receives ₹200 and Bhoomika receives ₹160.
Question 4
A family’s monthly expenditure on Food, Rent and Education is in the ratio 5 : 3 : 2. If the total expenditure is ₹60,000, find the amount spent on each category.
Solution
Monthly expenditure on Food, Rent and Education is in the ratio
= 5 : 3 : 2
Total Monthly Expenditure
= ₹60,000
Since the expenditure is divided in the ratio 5 : 3 : 2, we use the Formula to Divide a Quantity in a Given Ratio.
If a quantity Q is divided in the ratio A : B : C, then
First Share
= [A/(A + B + C)] × Q
Second Share
= [B/(A + B + C)] × Q
Third Share
= [C/(A + B + C)] × Q
Here,
Q = ₹60,000
A : B : C = 5 : 3 : 2
Food Expenditure
= [5/(5 + 3 + 2)] × 60,000
= (5/10) × 60,000
= ₹30,000
Rent Expenditure
= [3/(5 + 3 + 2)] × 60,000
= (3/10) × 60,000
= ₹18,000
Education Expenditure
= [2/(5 + 3 + 2)] × 60,000
= (2/10) × 60,000
= ₹12,000
Therefore,
Amount spent on Food = ₹30,000
Amount spent on Rent = ₹18,000
Amount spent on Education = ₹12,000.
Question 5:
The runs scored by Rohit and Virat in a tournament are in the ratio 7 : 9. Together they scored 640 runs. Find the runs scored by each player.
Solution
Runs scored by Rohit and Virat are in the ratio
= 7 : 9
Total Runs Scored
= 640
Since the total runs are distributed in the ratio 7 : 9, we use the Formula to Divide a Quantity in a Given Ratio.
If a quantity Q is divided in the ratio A : B, then
First Share
= [A/(A + B)] × Q
Second Share
= [B/(A + B)] × Q
Here,
Q = 640
A : B = 7 : 9
Runs scored by Rohit
= [7/(7 + 9)] × 640
= (7/16) × 640
= 280
Runs scored by Virat
= [9/(7 + 9)] × 640
= (9/16) × 640
= 360
Therefore,
Rohit scored 280 runs and Virat scored 360 runs in the tournament.
Question 6:
In an SSC coaching centre, the ratio of selected candidates to non-selected candidates is 3 : 5. If the total number of candidates is 320, find the number of selected candidates.
Solution
Ratio of Selected Candidates to Non-Selected Candidates
= 3 : 5
Total Number of Candidates
= 320
Since the total number of candidates is divided in the ratio 3 : 5, we use the Formula to Divide a Quantity in a Given Ratio.
If a quantity Q is divided in the ratio A : B, then
First Share
= [A/(A + B)] × Q
Second Share
= [B/(A + B)] × Q
Here,
Q = 320
A : B = 3 : 5
Number of Selected Candidates
= [3/(3 + 5)] × 320
= (3/8) × 320
= 120
Number of Non-Selected Candidates
= [5/(3 + 5)] × 320
= (5/8) × 320
= 200
Therefore,
Number of Selected Candidates = 120
Number of Non-Selected Candidates = 200.
Question 7:
In an RRB coaching centre, the ratio of boys, girls and teachers is 8 : 7 : 1. If the total number of people is 256, find the number of boys, girls and teachers.
Solution
Ratio of Boys : Girls : Teachers
= 8 : 7 : 1
Total Number of People
= 256
Since the total number of people is divided in the ratio 8 : 7 : 1, we use the Formula to Divide a Quantity in a Given Ratio.
If a quantity Q is divided in the ratio A : B : C, then
First Share
= [A/(A + B + C)] × Q
Second Share
= [B/(A + B + C)] × Q
Third Share
= [C/(A + B + C)] × Q
Here,
Q = 256
A : B : C = 8 : 7 : 1
Number of Boys
= [8/(8 + 7 + 1)] × 256
= (8/16) × 256
= 128
Number of Girls
= [7/(8 + 7 + 1)] × 256
= (7/16) × 256
= 112
Number of Teachers
= [1/(8 + 7 + 1)] × 256
= (1/16) × 256
= 16
Therefore,
Number of Boys = 128
Number of Girls = 112
Number of Teachers = 16.
Question 8:
A person’s income and savings are in the ratio 5 : 2. If his income is ₹50,000 per month, find his monthly expenditure.
Solution
Ratio of Income to Savings
= 5 : 2
Monthly Income
= ₹50,000
Using the ratio formula,
Income / Savings
= 5/2
50,000 / Savings
= 5/2
Savings
= (50,000 × 2)/5
= ₹20,000
Monthly Expenditure
= Income − Savings
= ₹50,000 − ₹20,000
= ₹30,000
Therefore,
Monthly Savings = ₹20,000
Monthly Expenditure = ₹30,000
Question 9:
The ratio of boys and girls in a Railway Recruitment coaching centre is 3 : 4. After 12 boys leave the coaching centre, the ratio of boys to girls becomes 2 : 3. Find the original number of boys and girls.
Answer
Given,
Ratio of Boys to Girls
= 3 : 4
This means that for every 3 boys, there are 4 girls.
Let the common multiplier be x.
Therefore,
Number of Boys = 3x
Number of Girls = 4x
According to the question, 12 boys leave the coaching centre.
Therefore,
New Number of Boys
= 3x − 12
Number of Girls remains unchanged
= 4x
The new ratio of boys to girls becomes 2 : 3.
Therefore,
(3x − 12) : 4x = 2 : 3
Using the ratio formula,
(3x − 12)/(4x) = 2/3
Cross-multiplying,
3(3x − 12) = 2(4x)
9x − 36 = 8x
9x − 8x = 36
x = 36
Now substitute the value of x.
Number of Boys
= 3 × 36
= 108
Number of Girls
= 4 × 36
= 144
Important Ratio and Proportion Resources
- Ratio and Proportion
- Basic Ratio Questions & Answers
- Ratio Formula with Examples and Explanations
- Proportion Questions and Answers with Solutions
- Unitary Method Questions and Answers with Solutions
- Direct Proportion Questions and Answers
- Inverse Proportion Questions & Answers with Solutions
- Ratio and Proportion Practice Questions with Answers
- Ratio and Proportion PYQs SSC, RRB, Banking & Defence Exams (Solved)