Ratio and Proportion for SSC CHSL: Download Free PDF & Practice Now

Preparing for the SSC CHSL exam? You are likely aiming for a desk job in a government ministry as an LDC or DEO. To get there, you have to score high in the Tier 1 exam, especially in Quantitative Aptitude. In the Math section, Ratio and Proportion is one of the most scoring topics. Why? Because if you master Ratio, you don’t just solve Ratio questions. You also automatically master topics like Ages, Partnership, Mixtures, and even Time & Work. Many students get scared when they see questions like “Find the fourth proportional” or “A bag contains 50p and 25p coins…” But you do not need to worry about it any more because here we have provided exam-level questions of ratio and proportion for SSC CHSL. Download the PDF for free and start practicing the questions.

Why is Ratio & Proportion Important for SSC CHSL?

In the SSC CHSL Tier 1 exam, this topic is a rank booster.

• The Foundation: It is the base of Arithmetic. 50% of the math paper uses Ratio logic.
• Direct Marks: You will definitely find 2 to 3 direct questions in the exam.
• Speed: Ratio questions can often be solved just by looking at the options. If the question asks for “A’s share” and A’s ratio is 7, the answer must be divisible by 7. This trick solves questions in 5 seconds!

Understanding the Concept

• Ratio (A:B): It is a comparison. If I have ₹10 and you have ₹20, our ratio is 1:2.
• Proportion (A:B:: C:D): It means two ratios are equal.
• Third Proportional: Uses the formula b² / a.
• Mean Proportional: Uses the formula √(axb).

Download Free PDF of Ratio & Proportion Questions for SSC CHSL

We have prepared a comprehensive PDF containing exam-level questions. We have covered all the favorite types of SSC CHSL, like Coin problems, Income-Expenditure, and Mean Proportional. Download it, save it, and practice these questions to build your speed.

Q1. If A : B = 2 : 3 and B : C = 5 : 7, find A : B : C.

(a) 10 : 15 : 21
(b) 10 : 15 : 20
(c) 2 : 3 : 7
(d) 10 : 20 : 21

Answer: (a) 10 : 15 : 21

Logic:
B is common in both ratios.
Make B equal.
Multiply first ratio by 5: 2 : 3 becomes 10 : 15.
Multiply second ratio by 3: 5 : 7 becomes 15 : 21.
So, A : B : C = 10 : 15 : 21.

Q2. Find the Fourth Proportional to 12, 16, and 18.

(a) 20
(b) 24
(c) 28
(d) 30

Answer: (b) 24

Logic:
12 : 16 :: 18 : x
Product of means = Product of extremes.
16 × 18 = 12 × x
288 = 12x
x = 24.

Q3. Find the Mean Proportional between 4 and 25.

(a) 12
(b) 10
(c) 15
(d) 8

Answer: (b) 10

Logic:
Mean proportional = square root of (a × b).
= square root of (4 × 25)
= square root of 100
= 10.

Q4. Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, they are in the ratio 12 : 23. Find the smaller number.

(a) 27
(b) 33
(c) 49
(d) 55

Answer: (b) 33

Logic:
Smaller number must be a multiple of 3.
Check 33 and 55.
33 − 9 = 24
55 − 9 = 46
Ratio = 24 : 46 = 12 : 23
So, smaller number = 33.

Q5. A bag contains Rs. 1, 50 paise, and 25 paise coins in the ratio 5 : 6 : 8. If the total amount is Rs. 240, find the number of 25 paise coins.

(a) 160
(b) 192
(c) 180
(d) 200

Answer: (b) 192

Logic:
Value ratio =
(5 × 1) : (6 × 0.5) : (8 × 0.25)
= 5 : 3 : 2

Total value units = 10
10x = 240
x = 24

Number of 25 paise coins = 8x
= 8 × 24
= 192.

Q6. If 3A = 4B = 5C, find A : B : C.

(a) 20 : 15 : 12
(b) 12 : 15 : 20
(c) 3 : 4 : 5
(d) 5 : 4 : 3

Answer: (a) 20 : 15 : 12

Logic:
Use hide-and-seek method.
Hide A: 4 × 5 = 20
Hide B: 3 × 5 = 15
Hide C: 3 × 4 = 12
So, A : B : C = 20 : 15 : 12.

Q7. The Third Proportional to 9 and 12 is:

(a) 16
(b) 18
(c) 20
(d) 24

Answer: (a) 16

Logic:
Third proportional formula:
c = (b × b) / a
= (12 × 12) / 9
= 144 / 9
= 16.

Q8. A sum of Rs. 300 is divided among P, Q, and R such that Q gets Rs. 30 more than P and R gets Rs. 60 more than Q. Find their ratio.

(a) 2 : 3 : 5
(b) 3 : 2 : 5
(c) 2 : 5 : 3
(d) 5 : 3 : 2

Answer: (a) 2 : 3 : 5

Logic:
Let P = x
Q = x + 30
R = x + 90

Total = x + (x + 30) + (x + 90)
3x + 120 = 300
3x = 180
x = 60

P = 60, Q = 90, R = 150
Ratio = 60 : 90 : 150
= 2 : 3 : 5.

Q9. The ratio of incomes of A and B is 5 : 6 and their expenditures are 3 : 4. If they save Rs. 1800 and Rs. 1600 respectively, find B’s income.

(a) Rs. 7200
(b) Rs. 6000
(c) Rs. 4800
(d) Rs. 3600

Answer: (a) Rs. 7200

Logic:
Income ratio = 5 : 6
Expenditure ratio = 3 : 4
Saving ratio = 1800 : 1600

Difference of cross-products:
(5 × 4) − (6 × 3) = 20 − 18 = 2 units

(1800 × 4) − (1600 × 3) = 7200 − 4800 = 2400

2 units = 2400
1 unit = 1200

B’s income = 6 units
= 6 × 1200
= Rs. 7200.

Q10. In a mixture of 60 liters, the ratio of milk and water is 2 : 1. How much water must be added to make the ratio 1 : 2?

(a) 40 liters
(b) 50 liters
(c) 60 liters
(d) 20 liters

Answer: (c) 60 liters

Logic:
Total mixture = 60 liters
Milk = 40 liters
Water = 20 liters

To make ratio 1 : 2,
If milk (1 part) = 40,
Water (2 parts) = 80

Water added = 80 − 20
= 60 liters.

How to Prepare Ratio Questions Easily?

Don’t calculate everything. Use smart tricks to save time. For that, we have provided some tips and tricks below.

• Check the Options First: This is the golden rule for SSC CHSL. If the question asks for “A’s Income” and the ratio is 5, the answer must be a number divisible by 5. Often, you can eliminate 2-3 options just by doing this.
• The “Hide and Seek” Trick: For questions like 3A = 4B = 5C, don’t find LCM. Just hide the variable you want to find and multiply the other two numbers. It’s instant.
• Memorize Formulas:
  • Mean Proportional = √ab
  • Third Proportional = b²/a
  • These questions come every year in CHSL Tier 1.
• 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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FAQs: Ratio & Proportion Questions for SSC CHSL