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SSC CPO Basic Ratio & Proportion

Study Material — 18 PYQs (2020–2020) · Concept Notes · Shortcuts

SSC CPO Basic Ratio & Proportion is a frequently tested subtopic — 18 previous year questions from 2020–2020 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

SSC CPO Basic Ratio & Proportion — Past Exam Questions

18 questions from actual SSC CPO papers · all shown free · click option to reveal solution

Exam Q 12020Previous Year Pattern

If 6 pens cost ₹90, what is the cost of 10 pens?

Exam Q 22020Previous Year Pattern

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

Exam Q 32020Previous Year Pattern

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

Exam Q 42020Previous Year Pattern

The ratio of ages of Aman and Bhuvan is 4:5. If Aman is 32 years old, what is Bhuvan's age?

Exam Q 52020Previous Year Pattern

In a mixture, the ratio of milk to water is 7:2. If the mixture contains 28 litres of milk, how many litres of water are in the mixture?

Exam Q 62020Previous Year Pattern

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

Exam Q 72020Previous Year Pattern

If 15 kg of rice costs ₹450, what is the cost of 25 kg of rice at the same rate?

Exam Q 82020Previous Year Pattern

In a mixture, the ratio of milk to water is 7:3. If the mixture contains 21 litres of milk, how many litres of water are in the mixture?

Exam Q 92020Previous Year Pattern

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

Exam Q 102020Previous 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 112020Previous Year Pattern

A sum of ₹1200 is divided among X, Y, and Z in the ratio 2:3:5. How much does Z receive?

Exam Q 122020Previous Year Pattern

The ratio of boys to girls in a school is 4:5. If there are 144 boys, how many total students are in the school?

Exam Q 132020Previous Year Pattern

Two quantities A and B are in the ratio 5:8. If A is increased by 40% and B is decreased by 25%, the new ratio becomes A':B'. What is the ratio A':B'?

Exam Q 142020Previous Year Pattern

Three numbers are in the ratio 2:3:4. If the sum of the largest and smallest numbers is 90, what is the sum of all three numbers?

Exam Q 152020Previous 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 162020Previous Year Pattern

In a mixture, the ratio of milk to water is 7:5. If 24 litres of water is added, the ratio becomes 7:9. How many litres of milk was in the original mixture?

Exam Q 172020Previous Year Pattern

A bag contains red, blue, and green balls in the ratio 4:5:6. If there are 60 more green balls than red balls, how many blue balls are in the bag?

Exam Q 182020Previous Year Pattern

The ratio of ages of two brothers is 3:5. After 6 years, their ages will be in the ratio 2:3. What is the sum of their current ages?

Concept Notes

Basic Ratio & Proportion— Rules & Concept

Core ConceptRead this first — the foundation of the topic

Basic Ratio & Proportion is the foundation of many SSC CGL problems. Think of ratio as a way to compare quantities. If you have 3 apples and 6 oranges, the ratio is 3:6, which simplifies to 1:2. This means for every 1 apple, there are 2 oranges. A ratio compares parts to parts. A proportion states that two ratios are equal. For example, 2:3 = 4:6 is a proportion because both ratios equal 2/3 when simplified.

Key Rules: (1) Ratios have no units - they are pure numbers. (2) Always simplify ratios by dividing by the HCF. (3) In a:b, 'a' is the first term and 'b' is the second term. (4) The ratio a:b can be written as the fraction a/b.

Formula BlockMemorise — at least one formula appears in every paper
• If a:b = c:d, then ad = bc (Cross multiplication rule)
• If a:b = m:n, then a = (m×total)/(m+n) and b = (n×total)/(m+n)

• For three quantities in ratio a:b:c, if total is T, then parts are aT/(a+b+c), bT/(a+b+c), cT/(a+b+c)

• Compound ratio of a:b and c:d is ac:bd

Exam PatternsWhat examiners ask — read before attempting PYQs
Common types include

age ratios, mixture problems, salary divisions, and proportion chains. Questions often involve finding actual values when ratios and total/difference are given

Powerful Shortcut - The K Method

When dealing with ratios, use 'K' as a multiplier. If ratio is 3:5, write quantities as 3K and 5K. This makes calculation much easier as you can find K first, then multiply.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Let numbers be 4K and 7K (using K method)

2
Step 2

Difference = 7K - 4K = 3K

3
Step 3

Given difference = 21, so 3K = 21

4
Step 4

Therefore K = 7

5
Step 5

First number = 4K = 4×7 = 28

6
Step 6

Second number = 7K = 7×7 = 49 Answer: 28 and 49 Worked Example 2: Rs. 850 is divided among A, B, C in ratio 2:3:5. Find each person's share.

1
Step 1

Ratio parts are 2, 3, 5

2
Step 2

Total ratio parts = 2+3+5 = 10

3
Step 3

A's share = (2/10) × 850 = Rs. 170

4
Step 4

B's share = (3/10) × 850 = Rs. 255

5
Step 5

C's share = (5/10) × 850 = Rs. 425 Answer: A gets Rs. 170, B gets Rs. 255, C gets Rs. 425 Shortcut for Direct Proportion: If A varies directly as B, and you know A₁, B₁, A₂, then B₂ = (A₂ × B₁)/A₁. Cross multiply and solve instantly. Trick for Inverse Proportion: If A varies inversely as B, then A₁B₁ = A₂B₂. When one increases, other decreases proportionally.

Exam TrapsCommon mistakes students make — avoid these

#1: Students often forget to check if the proportion is direct or inverse. In direct proportion, both quantities change in the same direction. In inverse proportion, they change in opposite directions.

Missing this distinction leads to wrong answers in 40% of cases. Always read the question twice to identify the relationship type.

Key Points to Remember

  • Ratio compares quantities without units, always simplify by dividing by HCF
  • Use K method: if ratio is a:b, write quantities as aK and bK for easy calculation
  • Cross multiplication rule: if a:b = c:d, then ad = bc
  • For ratio a:b with total T, parts are aT/(a+b) and bT/(a+b)
  • Direct proportion: A₁/B₁ = A₂/B₂, quantities change in same direction
  • Inverse proportion: A₁B₁ = A₂B₂, quantities change in opposite directions
  • Compound ratio of a:b and c:d equals ac:bd
  • In three-way ratio a:b:c with total T, each part is (ratio part × T)/(a+b+c)
  • Proportion means two ratios are equal: 2:3 = 4:6 is a valid proportion
  • When difference is given in ratio problems, subtract ratio terms to find multiplier

Exam-Specific Tips

  • Cross multiplication formula: if a/b = c/d, then ad = bc
  • Golden ratio value is approximately 1.618:1
  • In direct proportion, if A doubles, B also doubles
  • In inverse proportion, if A becomes half, B becomes double
  • Compound ratio formula: (a:b) combined with (c:d) gives ac:bd
  • For ratio a:b, percentage share of first term is a/(a+b) × 100%
  • Mean proportional between a and b is √(ab)
  • If three numbers are in continued proportion a:b:c, then b² = ac

60-Second Revision — Basic Ratio & Proportion

  • Remember: Use K method for all ratio problems - if ratio is a:b, quantities are aK and bK
  • Formula: Cross multiplication rule ad = bc when a:b = c:d
  • Formula: For total division, part = (ratio term × total)/sum of all ratio terms
  • Trap: Always check if proportion is direct (same direction) or inverse (opposite direction)
  • Shortcut: In difference problems, subtract ratio terms to find the multiplier K
  • Remember: Simplify ratios by HCF before starting calculations
  • Formula: Compound ratio of multiple ratios = multiply all first terms : multiply all second terms
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