Ratio and Proportion Questions for SSC MTS Exam: Download Free PDF

Are you preparing for the SSC MTS (Multi-Tasking Staff) or Railway exams? If yes, then you must know that Mathematics (Numerical Ability) is a very important section to clear your exam. Inside this math section, “Ratio and Proportion” is the most basic and powerful chapter. Many students run away from math because of big formulas. But here is the good news: Ratio and Proportion do not need tough formulas. It is a very simple topic based on our daily life calculations. Once you learn this chapter, you can easily solve other chapters like Age, Partnership, and Mixtures! In this blog, we have explained this topic in very simple words. We have also provided the top 10 exam-level questions that repeat every year.

What is Ratio and Proportion? (Explained in Simple Words)

You do not need to be a math expert to understand this. Let us understand it with a daily life example.

What is a Ratio? A ratio is simply a way to compare two things. For example, suppose you have 10 chocolates and your friend has 20 chocolates. If we want to compare them, we cut them to the smallest number. 10 and 20 can be cut by 10. So, it becomes 1 and 2. We write this as 1:2. This is the ratio! It simply means for every 1 chocolate you have, your friend has 2.

What is a Proportion? Proportion means that two ratios are exactly equal to each other. The sign for proportion is :: For example, if the ratio of boys to girls in Class A is 1:2, and in Class B it is also 1:2, we can say both classes are in proportion.

The only magic trick you need for this chapter is the “Unit Method”. Always find the value of “1 Unit” and you can solve any question in seconds!

Important Ratio & Proportion Questions for SSC MTS

Now that you know the basics, it is time to practice. Grab a pen and solve these top repeated Ratio and Proportion questions below. These perfectly match the SSC MTS exam level and format!

Q1. If A : B = 2 : 3 and B : C = 4 : 5, then find A : B : C.

(A) 2 : 3 : 5
(B) 8 : 12 : 15
(C) 6 : 12 : 15
(D) 8 : 10 : 15

Answer: (B) 8 : 12 : 15

Explanation: Here, ‘B’ is common in both. In the first ratio, B is 3. In the second, B is 4. Make them equal by multiplying.

Multiply A:B by 4 -> 8:12
Multiply B:C by 3 -> 12:15

Now B is 12 in both. So, A:B:C = 8:12:15.

Q2. Rs. 1000 is divided between Ram and Shyam in the ratio 3 : 2. What is the share of Ram?

(A) Rs. 400
(B) Rs. 500
(C) Rs. 600
(D) Rs. 700

Answer: (C) Rs. 600

Explanation: Total ratio = 3 + 2 = 5 units. Total money = Rs. 1000.

So, 5 units = 1000.
1 unit = 1000 / 5 = Rs. 200.

Ram has 3 units.
So, Ram’s share = 3 x 200 = Rs. 600.

Q3. Find the fourth proportion to 4, 8, and 12.

(A) 16
(B) 20
(C) 24
(D) 32

Answer: (C) 24

Explanation: Let the fourth proportion be ‘x’.

Rule: First x Fourth = Second x Third.

4 x ‘x’ = 8 x 12
4x = 96
x = 96 / 4 = 24.

Q4. Two numbers are in the ratio 4 : 5. If their sum is 72, find the larger number.

(A) 32
(B) 40
(C) 45
(D) 50

Answer: (B) 40

Explanation: Let numbers be 4 units and 5 units.

Total sum = 4 + 5 = 9 units.

We know the sum is 72.
So, 9 units = 72.
1 unit = 72 / 9 = 8.

Larger number is 5 units.
So, 5 x 8 = 40.

Q5. Find the mean proportion between 9 and 16.

(A) 12
(B) 14
(C) 25
(D) 144

Answer: (A) 12

Explanation: The formula for mean proportion is root of (a x b).

Square root of (9 x 16) = Square root of 144.

The square root of 144 is 12.

Q6. A bag has Rs. 1, 50-paisa, and 25-paisa coins in the ratio 2 : 3 : 4. If the total money is Rs. 90, find the number of 50-paisa coins.

(A) 40
(B) 60
(C) 80
(D) 100

Answer: (B) 60

Explanation: Value of coins:

Rs. 1 x 2 = Rs. 2
50p x 3 = Rs. 1.50
25p x 4 = Rs. 1

Total value in ratio = 2 + 1.50 + 1 = Rs. 4.50 units.

Total given money = Rs. 90.

4.50 units = 90.
1 unit = 90 / 4.50 = 20.

Number of 50-paisa coins = 3 units.
So, 3 x 20 = 60 coins.

Q7. The ratio of boys and girls in a school is 5 : 3. If there are 150 girls, what is the number of boys?

(A) 200
(B) 250
(C) 300
(D) 400

Answer: (B) 250

Explanation: Girls ratio is 3 units.

We know total girls are 150.

3 units = 150.
1 unit = 150 / 3 = 50.

Boys ratio is 5 units.

Number of boys = 5 x 50 = 250.

Q8. The income of A and B is in the ratio 3 : 4. Their expenses are in the ratio 2 : 3. If each saves Rs. 2000, find the income of A.

(A) Rs. 4000
(B) Rs. 6000
(C) Rs. 8000
(D) Rs. 10000

Answer: (B) Rs. 6000

Explanation: Income ratio = 3 : 4.
Expense ratio = 2 : 3.

Difference for A (Income – Expense) = 3 – 2 = 1 unit.
Difference for B (Income – Expense) = 4 – 3 = 1 unit.

Saving is 1 unit.

We know saving is Rs. 2000.
So, 1 unit = Rs. 2000.

Income of A = 3 units = 3 x 2000 = Rs. 6000.

Q9. Two numbers are in the ratio 2 : 3. If 5 is added to both, the ratio becomes 5 : 7. Find the smaller number.

(A) 10
(B) 20
(C) 30
(D) 40

Answer: (B) 20

Explanation: Let numbers be 2x and 3x.

(2x + 5) / (3x + 5) = 5 / 7

Cross multiply:

7(2x + 5) = 5(3x + 5)

14x + 35 = 15x + 25

15x – 14x = 35 – 25

x = 10.

Smaller number = 2x = 2 x 10 = 20.

Q10. The third proportion to 10 and 20 is?

(A) 30
(B) 40
(C) 50
(D) 60

Answer: (B) 40

Explanation: Formula for third proportion of a and b is (b x b) / a.

Here a = 10, b = 20.

(20 x 20) / 10 = 400 / 10 = 40.

5 Simple Tips to Prepare Ratio & Proportion

You do not need to be a math genius to score full marks in this topic. Just follow these easy tips:

• Always Find the 1 Unit Value: This is the master key! If you know the value of 1 unit, you can find the answer to any question by just multiplying.
• Check the Options: Sometimes, you do not even need to solve. If the question asks for A’s share and A’s ratio is 3, look at the options. The answer must be completely divisible by 3.
• Learn the Mean and Third Proportion Rules: SSC MTS asks direct questions on Mean Proportion, Third Proportion, and Fourth Proportion. Just memorize their small formulas.
• Don’t Use Long ‘x’ Methods: Using ‘x’ for every question takes too much time. Use the ratio difference method (like we did in the saving question above).
• Practice Previous Year Papers: SSC repeats its math questions a lot. The numbers might change, but the style of the question remains exactly the same.

Join our exclusive Telegram group for expert guidance, personalized tips, and real-time solutions to boost your SSC exam prep. [Click here to join now!]

SSC MTS More Related Articles
SSC MTS Syllabus	SSC MTS Cut Off
SSC MTS Salary	SSC MTS Exam Pattern
SSC MTS Previous Year Question Paper

FAQs: Ratio & Proportion Questions for SSC MTS

1. Is Ratio and Proportion a difficult chapter for SSC MTS?

No, not at all! It is one of the easiest and most scoring chapters. The questions are based on basic daily life calculations like dividing money or items.

2. How many questions come from this topic in the exam?

You can comfortably expect 1 to 2 direct questions from this chapter. Also, this chapter’s logic is used to solve other chapters like Data Interpretation (DI) and Time & Work.

3. Is there a negative marking in the SSC MTS Math section?

Good news! According to the latest SSC MTS pattern, Session 1 (which has Math and Reasoning) has NO negative marking. So, you can attempt all questions without fear.

4. Are these questions useful for Railway exams too?

Yes, 100%! The syllabus and question level for SSC MTS and Railway (Group D, NTPC, ALP) are almost the exact same. Practicing these will help in both.

5. What is the difference between Mean Proportion and Third Proportion?

Mean proportion between two numbers (a and b) is the square root of their product. Third proportion is calculated by dividing the square of the second number by the first number.