Study Material — 6 PYQs (2021–2021) · Concept Notes · Shortcuts
SBI Clerk Basic Ratio & Proportion is a frequently tested subtopic — 6 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.
SBI Clerk Basic Ratio & Proportion — Past Exam Questions
6 questions from actual SBI 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 4:5. If there are 12 more girls than boys, how many total students are in the class?
Exam Q 22021Previous Year Pattern
A recipe requires flour and sugar in the ratio 7:3. If 280 grams of flour is used, how much sugar (in grams) is needed?
Exam Q 32021Previous Year Pattern
If A:B = 3:5 and B:C = 2:3, what is A:B:C?
Exam Q 42021Previous Year Pattern
Two numbers are in the ratio 5:8. If their difference is 36, what is the sum of the two numbers?
Exam Q 52021Previous Year Pattern
A sum of money is divided among P, Q, and R in the ratio 3:4:5. If Q receives ₹2,400 more than P, what is the total sum?
Exam Q 62021Previous Year Pattern
The ratio of milk to water in a mixture is 5:3. If 16 litres of water is added, the ratio becomes 5:4. How many litres of milk was 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
Practice MCQs
Basic Ratio & Proportion — Practice Questions
7graded MCQs · easy to hard · full solution & trap analysis