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SSC CGL Basic Ratio & Proportion

Study Material — 33 PYQs (2018–2024) · Concept Notes · Shortcuts

SSC CGL Basic Ratio & Proportion is a frequently tested subtopic — 33 previous year questions from 2018–2024 papers are included below with concept notes, key rules and shortcut tricks.

33 PYQs
2018–2024
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Previous Year Questions

SSC CGL Basic Ratio & Proportion — Past Exam Questions

33 questions from actual SSC CGL papers · all shown free · click option to reveal solution

Exam Q 12024Previous Year Pattern

The ratio of ages of A and B is 3 : 4. If A is 18 years old, how old is B?

Exam Q 22024Previous Year Pattern

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

Exam Q 32024Previous Year Pattern

Two numbers are in the ratio 7:4. If their difference is 45, what is the larger number?

Exam Q 42024Previous Year Pattern

If A:B = 3:5 and B:C = 2:3, what is A:B:C?

Exam Q 52024Previous Year Pattern

If 12 books cost ₹480, what is the cost of 18 books?

Exam Q 62024Previous Year Pattern

The ratio of two numbers is 4 : 7. If their difference is 45, find the larger number.

Exam Q 72018Previous Year Pattern

The ratio of two numbers is 3:5. If each number is increased by 10, the new ratio becomes 5:7. What is the smaller of the two original numbers?

Exam Q 82020Previous Year Pattern

The ratio of ages of Amit and Bhavna is 5:7. If Amit is 20 years old, what is Bhavna's age?

Exam Q 92024Previous Year Pattern

A sum of money is divided among P, Q, and R in the ratio 2 : 3 : 5. If R receives ₹1000, what is the total sum?

Exam Q 102024Previous Year Pattern

The ratio of boys to girls in a class is 5:3. If there are 40 boys in the class, how many girls are there?

Exam Q 112024Previous Year Pattern

A sum of ₹1200 is divided among three people in the ratio 2:3:5. How much does the person with the largest share receive?

Exam Q 122019Previous Year Pattern

The ratio of ages of A and B is 5:7. If A is 15 years old, what is B's age?

Exam Q 132018Previous Year Pattern

The ratio of two numbers is 3:5. If 6 is added to each number, the ratio becomes 2:3. What is the smaller of the two numbers?

Exam Q 142024Previous Year Pattern

If x:y = 3:5 and y:z = 2:3, what is x:y:z?

Exam Q 152024Previous Year Pattern

The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is A's current age?

Exam Q 162024Previous Year Pattern

If x:y = 4:5 and y:z = 2:3, what is x:z?

Exam Q 172024Previous Year Pattern

A mixture contains milk and water in the ratio 3:2. If the mixture contains 15 litres of milk, how many litres of water are in the mixture?

Exam Q 182024Previous Year Pattern

A recipe requires flour and sugar in the ratio 5:2. If 350 grams of flour is used, how much sugar (in grams) is needed?

Exam Q 192024Previous Year Pattern

The ratio of boys to girls in a class is 7:5. If there are 84 boys, what is the total number of students in the class?

Exam Q 202024Previous Year Pattern

The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is the sum of their ages?

Exam Q 212024Previous Year Pattern

The ratio of boys to girls in a class is 4:5. If there are 12 more girls than boys, how many students are there in total?

Exam Q 222024Previous Year Pattern

In a mixture, the ratio of milk to water is 7:3. If 20 litres of water is added to the mixture, the ratio becomes 7:5. How many litres of milk were in the original mixture?

Exam Q 232024Previous Year Pattern

A sum of money is divided among A, B, and C in the ratio 5:7:8. If the difference between the shares of B and A is ₹600, what is the total sum of money?

Exam Q 242020Previous Year Pattern

A sum of money is divided among A, B, and C in the ratio 5:7:8. If the difference between the shares of B and A is ₹480, then what is the total sum of money divided?

Exam Q 252019Previous Year Pattern

A sum of money is divided among A, B, and C in the ratio 5:7:8. If the difference between the shares of B and A is ₹480, then what is the total sum of money divided?

Exam Q 262024Previous Year Pattern

Three containers have milk in the ratio 3:4:5. If 10 litres is transferred from the third container to the first, the new ratio becomes 5:4:3. What was the original quantity of milk in the second container?

Exam Q 272024Previous Year Pattern

Three containers have liquids in the ratio 2:3:4. If the second container has 15 litres more than the first, what is the total quantity of liquid in all three containers?

Exam Q 282024Previous Year Pattern

A sum of money is divided among A, B, and C in the ratio 5:7:8. If the difference between the shares of B and A is ₹480, what is the total sum of money?

Exam Q 292024Previous Year Pattern

The ratio of ages of father and son is 7:3. After 10 years, the ratio will be 9:5. What is the father's current age?

Exam Q 302024Previous Year Pattern

A mixture contains milk and water in the ratio 5:3. If 16 litres of water is added, the ratio becomes 5:7. How many litres of milk are in the original mixture?

Exam Q 312024Previous Year Pattern

A profit of ₹1200 is divided among three partners in the ratio 2:3:5. The difference between the largest and smallest share is:

Exam Q 322024Previous Year Pattern

The ratio of ages of two persons P and Q is 4:5. After 8 years, the ratio of their ages will be 6:7. What is the sum of their present ages?

Exam Q 332024Previous Year Pattern

Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes 5:7. Find the larger number.

Concept Notes

Basic Ratio & Proportion— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic

RATIO & PROPORTION — CORE CONCEPT A ratio compares two quantities of the same kind. If you have 3 apples and 5 oranges, the ratio of apples to oranges is 3:5. That's it. A ratio is just a way of saying 'how many times one quantity is of another.'

A proportion says that two ratios are equal. So if 3:5 = 6:10, these four numbers are in proportion. ---

2.Key Rules

Core rules you must know cold
1

A ratio a:b is the same as the fraction a/b.

2

Both terms of a ratio can be multiplied or divided by the same number. The ratio stays equal. So 4:6 = 2:3.

3

A ratio has no units. You cannot take a ratio of 3 kg and 5 metres.

4

Order matters. 3:5 is NOT the same as 5:3.

5

In a proportion a:b = c:d, the outer terms (a and d) are called EXTREMES. The inner terms (b and c) are called MEANS.

3.Formula Block

Memorise — at least one formula appears in every paper
If a:b = c:d, then a x d = b x c
(Product of Extremes = Product of Means)
Fourth Proportional: If a:b = c:x, then x = (b x c) / a
Third Proportional: If a:b = b:x, then x = b² / a
Mean Proportional: If a:x = x:b, then x = square root of (a x b)
Compound Ratio: (a:b) compounded with (c:d) = (a x c):(b x d)
Duplicate Ratio of a:b = a²:b²
Sub-duplicate Ratio of a:b = √a:√b
Triplicate Ratio of a:b = a³:b³

Proportion Rule (Cross Multiplication):

---

4.Exam Patterns

What examiners ask — read before attempting PYQs

— WHAT GETS ASKED SSC CGL asks ratio problems in these forms: - Dividing a sum in a given ratio - Finding the original quantities when ratio changes after adding/subtracting a number - Age problems using ratio - Income/Expenditure ratio problems - Finding third or fourth proportional - Mixture problems using ratio The most common question type: 'A sum is divided in ratio a:b. One part is X. Find the other part or total.' --- EXAM SHORTCUTS AND TRICKS TRICK 1 — DIVIDING A SUM If a total amount T is divided in ratio a:b: First part = T x a/(a+b) Second part = T x b/(a+b) Example: Divide Rs 880 in ratio 3:5 First part = 880 x 3/8 = Rs 330 Second part = 880 x 5/8 = Rs 550 TRICK 2 — RATIO CHANGE TRICK If ratio of A and B is a:b and you add x to both, the new ratio becomes p:q. Then: A = x(p - ratio coefficient) — solve via cross multiplication directly.

Set A = ak and B = bk, form equation. TRICK 3 — UNIT VALUE METHOD (UNITARY METHOD) Find the value of one unit (1 part), then scale up. This is the fastest method for almost all basic ratio problems. ---

5.Worked Example

Solve this step-by-step before moving on
1
Step 1

Add all ratio parts. 2 + 3 + 5 = 10 parts total.

2
Step 2

Value of 1 part = 1200 / 10 = Rs 120.

3
Step 3

A = 2 x 120 = Rs 240. B = 3 x 120 = Rs 360. C = 5 x 120 = Rs 600.

4
Step 4

Check: 240 + 360 + 600 = 1200. Correct. --- WORKED EXAMPLE 2 Question: The ratio of A to B is 3:4. If 6 is added to each, the new ratio becomes 4:5. Find A and B.

1
Step 1

Let A = 3k and B = 4k.

2
Step 2

After adding 6: (3k + 6)/(4k + 6) = 4/5

3
Step 3

Cross multiply: 5(3k + 6) = 4(4k + 6)

4
Step 4

15k + 30 = 16k + 24

5
Step 5

30 - 24 = 16k - 15k → k = 6

6
Step 6

A = 3 x 6 = 18. B = 4 x 6 = 24. Verify: (18+6):(24+6) = 24:30 = 4:5. Correct. ---

6.Exam Traps

Common mistakes students make — avoid these

— THE NUMBER ONE TRAP Students forget that when a ratio changes after adding or subtracting a value, they MUST set up the variable (let the ratio be 3k:4k) and form an equation. Many students directly assume k=1 and write A=3 and B=4. This is WRONG unless the question specifically states absolute values.

Always use 'k' as the multiplier. This single mistake causes maximum marks loss in ratio problems.

Key Points to Remember

  • A ratio a:b means a/b — it compares two quantities of the same kind and has no units.
  • Order matters in a ratio: 3:5 is NOT equal to 5:3.
  • In a proportion a:b = c:d, Product of Extremes = Product of Means, i.e., a x d = b x c.
  • Formula: Fourth Proportional to a, b, c is x = (b x c) / a.
  • Formula: Third Proportional to a and b is x = b² / a.
  • Formula: Mean Proportional between a and b is x = √(a x b).
  • Shortcut: To divide total T in ratio a:b, first part = T x a/(a+b), second part = T x b/(a+b).
  • Compound Ratio of a:b and c:d is (a x c):(b x d) — multiply numerators and denominators.
  • Duplicate Ratio of a:b = a²:b²; Triplicate Ratio = a³:b³; Sub-duplicate = √a:√b.
  • Always use 'k' as the multiplier (A = ak, B = bk) when ratio changes after addition or subtraction.

Exam-Specific Tips

  • If a:b = c:d, then (a+b):(a-b) = (c+d):(c-d) — this is called Componendo and Dividendo rule.
  • Mean Proportional between 4 and 16 is √(4 x 16) = √64 = 8.
  • Third Proportional to 3 and 6 is 6²/3 = 36/3 = 12.
  • Fourth Proportional to 2, 3, and 8 is (3 x 8)/2 = 12.
  • Duplicate ratio of 3:4 is 9:16; Triplicate ratio of 3:4 is 27:64.
  • If two numbers are in ratio a:b and their sum is S, the difference between them is S x (a-b)/(a+b).
  • Compound ratio of 2:3 and 4:5 and 6:7 is (2x4x6):(3x5x7) = 48:105 = 16:35.
Practice MCQs

Basic Ratio & Proportion — Practice Questions

27graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 27

All MCQs →
Practice 1easy

A sum of ₹1200 is divided between Raj and Priya in the ratio 3:5. How much does Priya receive?

Practice 2easy

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

Practice 3easy

Two numbers are in the ratio 7 : 9. If their difference is 8, find the larger number.

Practice 4easy

A sum of ₹1200 is divided between A and B in the ratio 2 : 3. How much does B receive?

Practice 5easy

The ratio of ages of Amit and Bhavna is 5:7. If Amit's age is 25 years, what is Bhavna's age?

Practice 6easy

If 4 pens cost ₹60, how much will 10 pens cost?

Practice 7easy

The ratio of boys to girls in a class is 4 : 5. If there are 20 boys, how many girls are there?

Practice 8easy

If x : 8 = 6 : 4, then the value of x is:

Practice 9easy

The ratio of boys to girls in a class is 5:3. If there are 40 boys in the class, how many girls are there?

Practice 10easy

If A:B = 7:5 and B:C = 5:4, then A:B:C is equal to:

Practice 11medium

The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is A's current age?

Practice 12medium

In a mixture, the ratio of milk to water is 7:3. If 20 litres of water is added, the ratio becomes 7:5. How many litres of milk are in the original mixture?

Practice 13medium

A certain amount is divided among X, Y, and Z in the ratio 1:2:3. If Z receives ₹300 more than X, what is Y's share?

Practice 14medium

The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is the sum of their ages?

Practice 15medium

A sum of money is divided among P, Q, and R in the ratio 3:5:7. If R receives ₹2100 more than P, what is the total sum?

Practice 16medium

The ratio of boys to girls in a school is 7:5. If there are 840 more boys than girls, how many girls are there in the school?

Practice 17medium

The ratio of present ages of two brothers is 4:5. After 8 years, the ratio will be 6:7. What is the sum of their present ages?

Practice 18medium

Two numbers are in the ratio 4:9. If their difference is 35, what is the larger number?

Practice 19medium

If A:B = 3:4 and B:C = 5:6, then A:B:C is equal to:

Practice 20hard

The ratio of ages of two persons P and Q is 4:5. After 8 years, the ratio of their ages will be 6:7. What is the difference in their current ages?

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60-Second Revision — Basic Ratio & Proportion

  • Remember: Always write ratio as ak:bk (not a:b directly) when the problem involves addition or subtraction changing the ratio.
  • Formula: Product of Extremes = Product of Means — use this to find any missing term in a proportion.
  • Formula: To divide amount T in ratio a:b:c, one part = T x (that ratio number)/(sum of all ratio numbers).
  • Formula: Mean Proportional between a and b = √(a x b); Third Proportional to a,b = b²/a.
  • Trap: Never take ratio of quantities with different units — quantities MUST be of the same kind.
  • Shortcut: Componendo-Dividendo — if a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d). Saves time in complex proportion questions.
  • Remember: Compound ratio = multiply all numerators together and all denominators together.
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