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SBI PO Basic Ratio & Proportion

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This page covers SBI PO Basic Ratio & Proportion with complete concept notes, 12 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Basic Ratio & Proportion— Rules & Concept

1.Core Concept

Read 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.

2.Formula Block

Memorise — 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

3.Exam Patterns

What 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.

4.Worked Example

Solve 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.

5.Exam Traps

Common 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

12graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

The ratio of boys to girls in a class is 2:3. If there are 10 boys, how many total students are in the class?

Practice 2easy

The ratio of ages of Arun and Bhavna is 5:3. If Arun is 20 years old, what is Bhavna's age?

Practice 3easy

A sum of ₹2400 is divided between Priya and Qureshi in the ratio 3:5. How much does Qureshi receive?

Practice 4easy

If x:y = 4:7 and y = 28, find the value of x.

Practice 5easy

If A:B = 5:8 and B:C = 4:7, find A:B:C.

Practice 6easy

A recipe requires flour and sugar in the ratio 7:2. If 350 grams of flour is used, how much sugar is needed?

Practice 7hard

Three containers have water in the ratio 2:3:4. If 5 litres is removed from each container, the ratio becomes 1:2:3. What is the total quantity of water in all three containers originally?

Practice 8hard

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 9hard

Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes 5:7. What is the larger of the two original numbers?

Practice 10hard

The ratio of ages of father and son is 7:3. After 10 years, the ratio will be 9:5. What is the present age of the father?

Practice 11hard

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

Practice 12hard

A profit of ₹1200 is divided among three partners in the ratio 2:3:5. The partner with the largest share uses his share to buy items at ₹40 per item. How many items can he buy?

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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