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SSC CHSL Basic Ratio & Proportion

Study Material — 1 PYQs (2018–2018) · Concept Notes · Shortcuts

SSC CHSL Basic Ratio & Proportion is a frequently tested subtopic — 1 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.

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2018–2018
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Previous Year Questions

SSC CHSL Basic Ratio & Proportion — Past Exam Questions

1 questions from actual SSC CHSL papers · all shown free · click option to reveal solution

Exam Q 12018Previous Year Pattern

The ratio of ages of Amit and Bhavna is 5:3. If Amit is 20 years older than Bhavna, what is Bhavna's present age?

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
Practice MCQs

Basic Ratio & Proportion — Practice Questions

22graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 22

All MCQs →
Practice 1easy

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?

Practice 2easy

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?

Practice 3easy

If 12 kg of rice costs ₹480, what is the cost of 18 kg of rice?

Practice 4easy

Two numbers are in the ratio 4:9. If their sum is 156, find the larger number.

Practice 5easy

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?

Practice 6easy

The ratio of speeds of two cars is 5:7. If the slower car travels 250 km, how far does the faster car travel in the same time?

Practice 7easy

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 8easy

Two numbers are in the ratio 7:5. If their difference is 18, what is the larger number?

Practice 9medium

A sum of money is divided among P, Q, and R in the ratio 4:5:6. If Q receives ₹500, what is the total sum?

Practice 10medium

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 11medium

If A:B = 7:5 and B:C = 3:4, what is A:C?

Practice 12medium

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 13medium

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

Practice 14medium

If A:B = 3:4 and B:C = 5:6, what is A:B:C?

Practice 15medium

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

Practice 16medium

The ratio of boys to girls in a class is 3:2. If there are 24 more boys than girls, how many girls are there?

Practice 17hard

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

Practice 18hard

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?

Practice 19hard

A sum of money is divided among P, Q, and R in the ratio 3:4:5. If R receives ₹600 more than P, what is the total sum?

Practice 20hard

The ratio of incomes of A and B is 5:4, and the ratio of their expenditures is 3:2. If each saves ₹1600, what is A's income?

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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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