Theory & Concepts
SSC CGL Ratio and Proportion Questions, Formulas & Tricks
Prepare Ratio and Proportion for SSC CGL with formulas, short tricks, solved examples, practice questions, PYQs, and free PDF notes for faster exam preparation.
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Practice Notes
20 min readDifficulty: Beginner to Intermediate
Ratio and proportion is the backbone of arithmetic. Whether you are solving ages, partnership, mixtures, or even geometry, the ability to manipulate ratios quickly is your greatest asset in Ssc cgl.
This topic goes beyond simple comparisons. In this guide, we will master Mean, Third, and Fourth proportion—concepts that appear frequently in recent CGL Tier-1 exams.
Learning path
- Basic ratio definitions
- Mean, Third, & Fourth proportion
- Componendo & Dividendo
- 10 standard solved problems
- Income & coin logic
1. Fundamental concepts
Ratio
A ratio is a comparison of two quantities of the same kind. The ratio of to is written as:
Proportion
Equality of two ratios is called proportion. If , then are in proportion.
2. Proportion master formulas
Mean proportion:
Third proportion:
Fourth proportion:
3. Solved examples
Question 01Standard pattern
If a : b = 2 : 3 and b : c = 4 : 5, find a : b : c.
8 : 12 : 15
2 : 3 : 5
8 : 10 : 15
4 : 6 : 15
Correct answer: a) 8 : 12 : 15
Solution
Balance the common term \( b \).
In \( a : b \), \( b \) is \( 3 \). In \( b : c \), \( b \) is \( 4 \).
Multiply \( a : b \) by \( 4 \to 8 : 12 \).
Multiply \( b : c \) by \( 3 \to 12 : 15 \).
Result = \( 8 : 12 : 15 \).
Question 02Standard pattern
Find the mean proportion between 4 and 64.
16
32
12
24
Correct answer: a) 16
Solution
Formula for Mean Proportion = \( \sqrt{a \times b} \).
Substitute: \( \sqrt{4 \times 64} \).
Calculation: \( \sqrt{256} = 16 \).
Result = \( 16 \).
Question 03Standard pattern
Find the third proportion to 16 and 36.
81
72
64
90
Correct answer: a) 81
Solution
Formula for Third Proportion = \( \frac{b^2}{a} \).
Substitute \( a = 16, b = 36 \).
Calculation: \( \frac{36 \times 36}{16} = \frac{1296}{16} \).
Result = \( 81 \).
Question 04Standard pattern
The ages of A and B are in the ratio 3 : 4. 10 years ago, their ages were in the ratio 4 : 7. Find their present ages.
18 and 24 years
12 and 16 years
15 and 20 years
21 and 28 years
Correct answer: a) 18 and 24 years
Solution
Let ages be \( 3x \) and \( 4x \).
Equation: \( \frac{3x - 10}{4x - 10} = \frac{4}{7} \).
Cross-multiply: \( 21x - 70 = 16x - 40 \).
\( 5x = 30 \implies x = 6 \).
Present ages: \( 3(6) = 18 \) and \( 4(6) = 24 \).
Question 05Standard pattern
A bag contains rs. 1, 50p and 25p coins in the ratio 5 : 6 : 8. If the total amount is rs. 240, find the number of 25p coins.
192
200
150
240
Correct answer: a) 192
Solution
Ratio of values: \( (5 \times 1) : (6 \times 0.5) : (8 \times 0.25) \).
\( 5 : 3 : 2 \).
Total parts: \( 5 + 3 + 2 = 10 \).
Value of 25p coins: \( \frac{2}{10} \times 240 = rs. 48 \).
Number of 25p coins: \( 48 \times 4 = 192 \).
Question 06Standard pattern
If x : y = 3 : 4, find (5x + 3y) : (7x - 2y).
27 : 13
15 : 12
20 : 13
25 : 14
Correct answer: a) 27 : 13
Solution
Substitute \( x = 3, y = 4 \) directly into the expression.
Numerator: \( 5(3) + 3(4) = 15 + 12 = 27 \).
Denominator: \( 7(3) - 2(4) = 21 - 8 = 13 \).
Result = \( 27 : 13 \).
Question 07Standard pattern
An amount of rs. 1050 is distributed among A, B and C in the ratio 2 : 5 : 8. What is the difference between the shares of C and A?
rs. 420
rs. 350
rs. 400
rs. 380
Correct answer: a) rs. 420
Solution
Total parts: \( 2 + 5 + 8 = 15 \).
Difference between C and A in parts: \( 8 - 2 = 6 \).
Calculation: \( \frac{6}{15} \times 1050 \).
\( \frac{2}{5} \times 1050 = 2 \times 210 = 420 \).
Result = \( rs. 420 \).
Question 08Standard pattern
What number must be added to each of 6, 15, 20 and 43 to make them proportional?
3
4
2
5
Correct answer: a) 3
Solution
Equation: \( \frac{6+x}{15+x} = \frac{20+x}{43+x} \).
Cross-multiply: \( (6+x)(43+x) = (15+x)(20+x) \).
\( 258 + 49x + x^2 = 300 + 35x + x^2 \).
\( 14x = 42 \implies x = 3 \).
Result = \( 3 \).
Question 09Standard pattern
If 30% of A = 0.25 of B = 1/5 of C, then A : B : C is:
10 : 12 : 15
3 : 4 : 5
12 : 10 : 15
15 : 12 : 10
Correct answer: a) 10 : 12 : 15
Solution
Rewrite as fractions: \( \frac{3}{10} A = \frac{1}{4} B = \frac{1}{5} C \).
Set equal to constant k: \( A = \frac{10}{3}k, B = 4k, C = 5k \).
Ratio: \( \frac{10}{3} : 4 : 5 \).
Multiply by 3: \( 10 : 12 : 15 \).
Result = \( 10 : 12 : 15 \).
Question 010Standard pattern
Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the new ratio is 12 : 23. Find the smaller number.
33
27
40
45
Correct answer: a) 33
Solution
Let numbers be \( 3x \) and \( 5x \).
Equation: \( \frac{3x - 9}{5x - 9} = \frac{12}{23} \).
Cross-multiply: \( 69x - 207 = 60x - 108 \).
\( 9x = 99 \implies x = 11 \).
Smaller number: \( 3(11) = 33 \).
