Study Material — 18 PYQs (2021–2021) · Concept Notes · Shortcuts
IBPS Clerk Basic Ratio & Proportion is a frequently tested subtopic — 18 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.
IBPS Clerk Basic Ratio & Proportion — Past Exam Questions
18 questions from actual IBPS Clerk papers · all shown free · click option to reveal solution
Exam Q 12021Previous 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 22021Previous Year Pattern
Two numbers are in the ratio 7:5. If their difference is 18, what is the larger number?
Exam Q 32021Previous Year Pattern
The ratio of speeds of two cars is 4:5. If the slower car travels 240 km, how far does the faster car travel in the same time?
Exam Q 42021Previous Year Pattern
If A:B = 3:4 and B:C = 5:6, what is A:B:C?
Exam Q 52021Previous Year Pattern
A sum of ₹1200 is divided among X, Y, and Z in the ratio 2:3:5. How much does Y receive?
Exam Q 62021Previous Year Pattern
If 12 workers can complete a job in 8 days, how many days will 16 workers take to complete the same job?
Exam Q 72021Previous Year Pattern
The speeds of two cars are in the ratio 5:8. If the slower car travels 250 km in a certain time, how far does the faster car travel in the same time?
Exam Q 82021Previous Year Pattern
A sum of ₹1200 is divided between X and Y in the ratio 3:5. How much does Y receive?
Exam Q 92021Previous Year Pattern
A recipe requires flour and sugar in the ratio 7:3. If 210 grams of flour is used, how much sugar (in grams) is needed?
Exam Q 102021Previous Year Pattern
The ratio of ages of A and B is 5:7. If the difference between their ages is 8 years, what is A's age?
Exam Q 112021Previous Year Pattern
If 15 workers can complete a task in 12 days, how many days will 18 workers take to complete the same task (assuming uniform work rate)?
Exam Q 122021Previous Year Pattern
The ratio of boys to girls in a class is 4:5. If there are 36 boys, how many total students are in the class?
Exam Q 132021Previous Year Pattern
Three containers have milk in the ratio 2:3:4. If 5 litres is transferred from the third container to the first, the new ratio becomes 3:3:4. What was the original quantity of milk in the second container?
Exam Q 142021Previous Year Pattern
A, B, and C invested money in a business in the ratio 4:5:6. At the end of the year, the profit is ₹45,000. If the profit is distributed in the ratio of their investments, how much more profit does C receive compared to A?
Exam Q 152021Previous 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 162021Previous Year Pattern
Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes 5:7. What is the sum of the original two numbers?
Exam Q 172021Previous Year Pattern
The ratio of ages of father and son is 7:2. After 10 years, the ratio will be 9:4. What is the father's current age?
Exam Q 182021Previous 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?
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