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IBPS RRB PO Basic Ratio & Proportion

Study Material — 18 PYQs (2022–2022) · Concept Notes · Shortcuts

IBPS RRB PO Basic Ratio & Proportion is a frequently tested subtopic — 18 previous year questions from 2022–2022 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

IBPS RRB PO Basic Ratio & Proportion — Past Exam Questions

18 questions from actual IBPS RRB PO papers · all shown free · click option to reveal solution

Exam Q 12022Previous Year Pattern

Two numbers are in the ratio 5:8. If their difference is 24, what is the larger number?

Exam Q 22022Previous Year Pattern

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

Exam Q 32022Previous Year Pattern

If 3 pens cost ₹45, how much will 8 pens cost?

Exam Q 42022Previous Year Pattern

The ratio of boys to girls in a class is 3:2. If there are 15 boys, how many girls are there?

Exam Q 52022Previous Year Pattern

A sum of money is divided between X and Y in the ratio 4:6. If X receives ₹800, what is the total sum?

Exam Q 62022Previous Year Pattern

If A:B = 2:3 and B:C = 4:5, what is A:C?

Exam Q 72022Previous 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 82022Previous 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 92022Previous Year Pattern

A sum of ₹2400 is divided among P, Q, and R in the ratio 2:3:4. How much more does R receive than P?

Exam Q 102022Previous Year Pattern

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

Exam Q 112022Previous Year Pattern

A recipe requires flour and sugar in the ratio 7:3. If 280 grams of flour is used, how many grams of sugar are needed?

Exam Q 122022Previous Year Pattern

Three numbers are in the ratio 2:4:5. If the sum of the smallest and largest numbers is 84, what is the middle number?

Exam Q 132022Previous Year Pattern

Two numbers are in the ratio 7:9. If each number is increased by 20, the ratio becomes 4:5. Find the larger number.

Exam Q 142022Previous Year Pattern

In a school, the ratio of boys to girls is 5:7. If 20 more girls are admitted, the ratio becomes 5:8. How many boys are there in the school?

Exam Q 152022Previous 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 162022Previous Year Pattern

The ratio of incomes of A and B is 9:7, and the ratio of their expenditures is 4:3. If each saves ₹2000 per month, what is A's monthly income?

Exam Q 172022Previous Year Pattern

The ratio of ages of A, B, and C is 4:5:6. If the sum of their ages is 90 years, find the difference between the ages of C and A.

Exam Q 182022Previous Year Pattern

A sum of money is divided among P, Q, and R in the ratio 2:3:5. If R receives ₹1500 more than P, what is the total sum?

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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