ZE
ZESTEXAM

SSC GD Constable Basic Ratio & Proportion

Study Material · Concept Notes · Shortcuts

This page covers SSC GD Constable Basic Ratio & Proportion with complete concept notes, 18 graded practice MCQs, key points and exam-specific tips. Free to study.

0 PYQs
none yet
18 Practice
MCQs
10 Key Points
to remember
Free
no login needed
Take Free Mock →Full Practice Set
Also for:CGLCHSLMTSCPO
PYQs
0
Practice
18
Key Points
10
Access
Free
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

18graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

If x:y = 2:3 and y:z = 6:5, find x:z.

Practice 2easy

If A:B = 7:5 and B:C = 5:3, find A:C.

Practice 3easy

If 6 pens cost ₹90, what is the cost of 10 pens?

Practice 4easy

The ratio of boys to girls in a class is 5:3. If there are 40 boys, how many girls are there?

Practice 5easy

A sum of ₹1200 is divided between Raj and Priya in the ratio 3:5. How much does Priya get?

Practice 6easy

The ratio of length to breadth of a rectangle is 4:3. If the length is 20 cm, what is the breadth?

Practice 7medium

If 4 workers can complete a task in 12 days, how many days will 6 workers take to complete the same task (assuming equal work rate)?

Practice 8medium

The ratio of ages of A and B is 5:7. If A is 15 years old, what is B's age?

Practice 9medium

A sum of ₹1200 is divided between X and Y in the ratio 3:5. How much does Y receive?

Practice 10medium

Three numbers are in the ratio 2:3:5. If their sum is 100, what is the largest number?

Practice 11medium

The ratio of boys to girls in a class is 4:5. If there are 20 boys, what is the total number of students?

Practice 12medium

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?

Practice 13hard

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 ₹480, what is the total sum of money?

Practice 14hard

Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes 5:7. Find the larger number.

Practice 15hard

The ratio of ages of father and son is 7:3. After 6 years, the ratio will be 2:1. What is the father's current age?

Practice 16hard

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?

Practice 17hard

Three containers have liquids in the ratio 2:3:4 by volume. If the second container has 15 litres more than the first, what is the total volume in all three containers?

Practice 18hard

A profit of ₹2400 is divided among three partners in the ratio 5:7:12. The third partner's share is how much more than the first partner's share?

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
Partnership→
Studied the notes? Now test yourself
See how Basic Ratio & Proportion appears in the real SSC GD Constable paper
Full timed mock · Instant All-India percentile · Free
Start Free Mock →Practice Panel
✓ Free forever for basic prep✓ No app download✓ Real exam-pattern questions✓ 12,000+ aspirants
Test Basic Ratio & Proportion under exam conditions
Free SSC GD Constable mock · instant rank · no login
Free Mock →