CDS Basic Ratio & Proportion — Study Material, 33 PYQs & Practice MCQs | ZestExam
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CDS Basic Ratio & Proportion
Study Material — 33 PYQs (2018–2024) · Concept Notes · Shortcuts
CDS Basic Ratio & Proportion is a frequently tested subtopic — 33 previous year questions from 2018–2024 papers are included below with concept notes, key rules and shortcut tricks.
The ratio of ages of A and B is 5:7. If A is 15 years old, what is B's age?
Exam Q 32024Previous Year Pattern
A sum of ₹1200 is divided among three people in the ratio 2:3:5. How much does the person with the largest share receive?
Exam Q 42024Previous Year Pattern
The ratio of boys to girls in a class is 5:3. If there are 40 boys in the class, how many girls are there?
Exam Q 52024Previous Year Pattern
A sum of money is divided among P, Q, and R in the ratio 2 : 3 : 5. If R receives ₹1000, what is the total sum?
Exam Q 62018Previous Year Pattern
The ratio of two numbers is 3:5. If each number is increased by 10, the new ratio becomes 5:7. What is the smaller of the two original numbers?
Exam Q 72024Previous Year Pattern
The ratio of two numbers is 4 : 7. If their difference is 45, find the larger number.
Exam Q 82024Previous Year Pattern
If 12 books cost ₹480, what is the cost of 18 books?
Exam Q 92024Previous Year Pattern
If A:B = 3:5 and B:C = 2:3, what is A:B:C?
Exam Q 102024Previous Year Pattern
Two numbers are in the ratio 7:4. If their difference is 45, what is the larger number?
Exam Q 112024Previous Year Pattern
If A : B = 3 : 5 and B : C = 2 : 3, find A : B : C.
Exam Q 122024Previous Year Pattern
The ratio of ages of A and B is 3 : 4. If A is 18 years old, how old is B?
Exam Q 132024Previous 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 142024Previous Year Pattern
If x:y = 3:5 and y:z = 2:3, what is x:y:z?
Exam Q 152024Previous Year Pattern
The ratio of boys to girls in a class is 7:5. If there are 84 boys, what is the total number of students in the class?
Exam Q 162024Previous Year Pattern
If x:y = 4:5 and y:z = 2:3, what is x:z?
Exam Q 172024Previous Year Pattern
A recipe requires flour and sugar in the ratio 5:2. If 350 grams of flour is used, how much sugar (in grams) is needed?
Exam Q 182024Previous Year Pattern
A mixture contains milk and water in the ratio 3:2. If the mixture contains 15 litres of milk, how many litres of water are in the mixture?
Exam Q 192018Previous Year Pattern
The ratio of two numbers is 3:5. If 6 is added to each number, the ratio becomes 2:3. What is the smaller of the two numbers?
Exam Q 202024Previous Year Pattern
The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is A's current age?
Exam Q 212024Previous 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 222024Previous Year Pattern
In a mixture, the ratio of milk to water is 7:3. If 20 litres of water is added to the mixture, the ratio becomes 7:5. How many litres of milk were in the original mixture?
Exam Q 232024Previous Year Pattern
Two numbers are in the ratio 3:5. If each number is increased by 10, the ratio becomes 5:7. Find the larger number.
Exam Q 242024Previous Year Pattern
A profit of ₹1200 is divided among three partners in the ratio 2:3:5. The difference between the largest and smallest share is:
Exam Q 252024Previous Year Pattern
The ratio of ages of two persons P and Q is 4:5. After 8 years, the ratio of their ages will be 6:7. What is the sum of their present ages?
Exam Q 262024Previous Year Pattern
Three containers have milk in the ratio 3:4:5. If 10 litres is transferred from the third container to the first, the new ratio becomes 5:4:3. What was the original quantity of milk in the second container?
Exam Q 272024Previous 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 282020Previous 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 ₹480, then what is the total sum of money divided?
Exam Q 292024Previous Year Pattern
Three containers have liquids in the ratio 2:3:4. If the second container has 15 litres more than the first, what is the total quantity of liquid in all three containers?
Exam Q 302024Previous Year Pattern
The ratio of ages of father and son is 7:3. After 10 years, the ratio will be 9:5. What is the father's current age?
Exam Q 312024Previous 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 322024Previous 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 ₹480, what is the total sum of money?
Exam Q 332019Previous 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 ₹480, then what is the total sum of money divided?
Concept Notes
Basic Ratio & Proportion— Rules & Concept
💡
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.
🔢
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
📊
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
✏️Worked Example 1
1
Let numbers be 4K and 7K (using K method)
2
Difference = 7K - 4K = 3K
3
Given difference = 21, so 3K = 21
4
Therefore K = 7
5
First number = 4K = 4×7 = 28
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
Ratio parts are 2, 3, 5
2
Total ratio parts = 2+3+5 = 10
3
A's share = (2/10) × 850 = Rs. 170
4
B's share = (3/10) × 850 = Rs. 255
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.
Common Mistake #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
27graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 27
If A:B = 7:5 and B:C = 5:4, then A:B:C is equal to:
Practice 2easy
A sum of ₹1200 is divided between Raj and Priya in the ratio 3:5. How much does Priya receive?
Practice 3easy
The ratio of boys to girls in a class is 4 : 5. If there are 20 boys, how many girls are there?
Practice 4easy
If 4 pens cost ₹60, how much will 10 pens cost?
Practice 5easy
If x : 8 = 6 : 4, then the value of x is:
Practice 6easy
The ratio of boys to girls in a class is 5:3. If there are 40 boys in the class, how many girls are there?
Practice 7easy
If A : B = 3 : 5 and B : C = 2 : 3, then find A : B : C.
Practice 8easy
The ratio of ages of Amit and Bhavna is 5:7. If Amit's age is 25 years, what is Bhavna's age?
Practice 9easy
A sum of ₹1200 is divided between A and B in the ratio 2 : 3. How much does B receive?
Practice 10easy
Two numbers are in the ratio 7 : 9. If their difference is 8, find the larger number.
Practice 11medium
The ratio of ages of A and B is 5:7. If A is 15 years younger than B, what is A's current age?
Practice 12medium
The ratio of boys to girls in a school is 7:5. If there are 840 more boys than girls, how many girls are there in the school?
Practice 13medium
A sum of money is divided among P, Q, and R in the ratio 3:5:7. If R receives ₹2100 more than P, what is the total sum?
Practice 14medium
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?
Practice 15medium
A certain amount is divided among X, Y, and Z in the ratio 1:2:3. If Z receives ₹300 more than X, what is Y's share?
Practice 16medium
In a mixture, the ratio of milk to water is 7:3. If 20 litres of water is added, the ratio becomes 7:5. How many litres of milk are in the original mixture?
Practice 17medium
The ratio of present ages of two brothers is 4:5. After 8 years, the ratio will be 6:7. What is the sum of their present ages?
Practice 18medium
Two numbers are in the ratio 4:9. If their difference is 35, what is the larger number?
Practice 19medium
If A:B = 3:4 and B:C = 5:6, then A:B:C is equal to:
Practice 20hard
The ratio of boys to girls in a school is 5:7. If there are 480 more girls than boys, how many boys are there in the school?
7 more practice questions in the Study Panel
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