Ratio and Proportion Questions for RRB NTPC: Download Free PDF

Dreaming of working in the Indian Railways? Whether you want to be a Station Master or a Clerk, the RRB NTPC exam is your golden ticket. Preparation for this exam is not easy. Most candidates fail due to less preparation or scoring low in maths. In the Quantitative Aptitude section, Ratio and Proportion is not just a topic; it is the backbone of Arithmetic. Why do I say that? Because if you understand ratios, you can easily solve questions on Ages, partnerships, Mixtures, and even Time & Work without using long formulas. Many students get confused when they see questions like “Find the third proportional” or “Divide ₹500 in the ratio 2:3.” To help you master this rank-boosting topic, we have analyzed previous Railway papers and collected the most important questions. We have compiled them into a free PDF that you can download below.

Why is Ratio & Proportion Important for RRB NTPC?

In both CBT-1 and CBT-2, this topic is a superhero.

• Foundation of Math: If your Ratio concept is strong, you automatically become good at Data Interpretation (DI) and Profit & Loss.
• Direct Questions: You can expect 2 to 3 direct questions in the exam.
• Option Elimination: The best part about Ratio questions is that you can often solve them just by checking the options (using divisibility rules) without solving the whole problem.

Understanding the Concept

Before you start practicing, let’s clear the basics.

• Ratio (A:B): It is just a comparison. If you have 2 toffees and I have 3, our ratio is 2:3.
• Proportion (A:B :: C:D): It means two ratios are equal. Think of it as a balance scale.
• Mean Proportional: The middle number between two numbers. Formula: sqrt{ab}.

Download Free PDF of Ratio & Proportion Questions for RRB NTPC

We have prepared a comprehensive PDF containing exam-level questions. We have chosen questions that cover all types—Coins, Ages, Proportions, and Income-Expenditure. Download it, save it, and practice these questions to build your speed.

Q1. If A : B = 3 : 4 and B : C = 8 : 9, then find A : B : C.

(a) 3 : 4 : 5
(b) 6 : 8 : 9
(c) 3 : 8 : 9
(d) 9 : 8 : 6

Answer: (b) 6 : 8 : 9

Logic:
B is common in both ratios.
Make B equal in both ratios.
Multiply the first ratio by 2.
3 : 4 becomes 6 : 8.
Second ratio is 8 : 9.
So, A : B : C = 6 : 8 : 9.

Q2. Find the Mean Proportional between 9 and 16.

(a) 12
(b) 144
(c) 10
(d) 14

Answer: (a) 12

Logic:
Mean Proportional = square root of (a × b).
= square root of (9 × 16)
= square root of 144
= 12.

Q3. Find the Third Proportional to 4 and 6.

(a) 8
(b) 9
(c) 10
(d) 12

Answer: (b) 9

Logic:
Formula for third proportional:
c = (b × b) / a
= (6 × 6) / 4
= 36 / 4
= 9.

Q4. If 10, 20, x, and 40 are in proportion, find x.

(a) 15
(b) 25
(c) 30
(d) 20

Answer: (d) 20

Logic:
Product of extremes = Product of means.
10 × 40 = 20 × x
400 = 20x
x = 20.

Q5. Divide Rs. 1200 between A, B, and C in the ratio 2 : 3 : 5.

(a) 200, 300, 700
(b) 240, 360, 600
(c) 250, 350, 600
(d) 200, 400, 600

Answer: (b) 240, 360, 600

Logic:
Total ratio = 2 + 3 + 5 = 10.
Value of 1 unit = 1200 / 10 = 120.
A = 2 × 120 = 240
B = 3 × 120 = 360
C = 5 × 120 = 600.

Q6. A bag contains Rs. 1, 50 paise, and 25 paise coins in the ratio 2 : 3 : 4. If the total value is Rs. 180, find the number of 50 paise coins.

(a) 60
(b) 90
(c) 120
(d) 150

Answer: (c) 120

Logic:
Value ratio =
(2 × 1) : (3 × 0.5) : (4 × 0.25)
= 2 : 1.5 : 1

Total value units = 4.5
4.5x = 180
x = 40

Number of 50 paise coins = 3x
= 3 × 40
= 120.

Q7. The ratio of incomes of A and B is 3 : 4 and their expenditures are 2 : 3. If both save Rs. 200, find A’s income.

(a) Rs. 600
(b) Rs. 800
(c) Rs. 500
(d) Rs. 900

Answer: (a) Rs. 600

Logic:
Difference between income and expenditure ratios is same.
For A: 3 − 2 = 1 unit
For B: 4 − 3 = 1 unit

So, 1 unit = saving = Rs. 200.
A’s income = 3 units = 3 × 200 = Rs. 600.

Q8. The Fourth Proportional to 4, 8, and 12 is:

(a) 16
(b) 20
(c) 24
(d) 32

Answer: (c) 24

Logic:
4 : 8 :: 12 : x
Product of means = Product of extremes.
8 × 12 = 4 × x
96 = 4x
x = 24.

Q9. Two numbers are in the ratio 3 : 5. If 10 is added to each, the ratio becomes 5 : 7. Find the numbers.

(a) 10, 20
(b) 15, 25
(c) 12, 20
(d) 18, 30

Answer: (b) 15, 25

Logic:
Difference in ratio increases by same amount.
3 to 5 = 2 units
5 to 7 = 2 units

So, 2 units = 10
1 unit = 5

Numbers are:
3 × 5 = 15
5 × 5 = 25.

Q10. If 2A = 3B = 4C, find A : B : C.

(a) 2 : 3 : 4
(b) 4 : 3 : 2
(c) 6 : 4 : 3
(d) 3 : 4 : 6

Answer: (c) 6 : 4 : 3

Logic:
Hide A, multiply remaining numbers: 3 × 4 = 12
Hide B, multiply remaining numbers: 2 × 4 = 8
Hide C, multiply remaining numbers: 2 × 3 = 6

Ratio = 12 : 8 : 6
Simplify = 6 : 4 : 3.

How to Prepare Ratio and Proportion Questions Easily?

Ratio is all about tricks. You don’t always need to calculate.

• The “Hide and Seek” Method: To solve questions like 2A = 3B, just cover A with your finger and multiply the numbers next to B and C. That’s your value for A. It’s the fastest trick.
• Check Options First: If the question asks for “A’s share” and A’s ratio is 3, the answer must be divisible by 3. Check the options. If only one option is divisible by 3, mark it and move on!
• Memorize Proportional Formulas:
  • Mean Proportional = √ab
  • Third Proportional = b²/a
  • These direct formulas save time.
• Practice with Topic Tests: Reading is not enough. You must solve. Attempt our Free Topic Tests to increase your calculation speed.

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