Ratio & Proportion PYQs for UPSC (2011-2024) | Solved Questions & PDF Download

Master Ratio & Proportion concepts for UPSC with solved Previous Year Questions (PYQs) from 2011 to 2024. This comprehensive guide provides detailed solutions, shortcut formulas, and a free downloadable PDF to help you crack all types of ratio and proportion problems in UPSC CSAT.

Why Ratio & Proportion Matters in UPSC CSAT?

Ratio & Proportion questions are frequently asked in UPSC CSAT (Paper II) to test:

· Your ability to compare quantities mathematically

· Understanding of direct and inverse relationships

· Skills in solving real-world scenario-based problems

This page covers all ratio & proportion PYQs with smart calculation techniques.

Year-Wise Ratio & Proportion PYQs (2011-2024)

Q1. In a rare coin collection, there is one gold for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1: 2. Based on the information, the total number of coins in the collection now becomes. [CSAT 2013]

(a) 90

(b) 80

(d) 50

Solution:

Given that,

There is one gold for every three non-gold coins.

10 more gold coins are added to the collection

The ratio of gold coins to non-gold coins would be 1: 2.

Now,

Let gold coins be G

Non gold coins be N

So,

G : N = 1 : 3......(i)

G = 3N.......(ii)

Adding 10 more gold coins

(G + 10) : N = 1 : 2

(G + 10) : 3G = 1 : 2......(iii)

2G + 20 = 3G

G = 20.....(iv)

Thus N = 3 x 20 = 60

Total coins = 60 + 20 = 80

Also 10 more gold coins added = 80 + 10 = 90

Hence option (a) is correct

Q2. The monthly incomes of Peter and Paul are in the ratio of 4: 3. Their expenses are in the ratio of 3: 2. If each save Rs. 6000 at end of the month, their monthly incomes respectively are (in Rs.) [CSAT 2015]

(a) 24000 and 18000

(b) 28000 and 21000

(d) 34000 and 26000

Solution:

Given that,

The monthly incomes of Peter and Paul are in the ratio of 4: 3.

Their expenses are in the ratio of 3: 2.

Each save Rs. 6000 at end of the month

Now,

Let income be I and expenses be E

Income = 4I : 3I

Expenses = 3E : 2E

4I - 3E = 6000.....(i)

3I - 2E = 6000.....(ii)

Thus by solving the equation (i) and (ii)

I = E = 6000

Therefore, income of peter = 4 x 6000 = 24000

Income of Paul = 3 x 6000 = 18000

Hence option (a) is correct

Q3. The monthly incomes of X and Y are in the ratio of 4:3 and their monthly expenses are in the ratio of 3 2. However, each saves Rs. 6,000 per month. What is their total monthly income? [CSAT 2017]

(a) Rs. 28,000

(b) Rs. 42,000

(d) Rs. 84,000

Solution:

Given that,

The monthly incomes of X and Y are in the ratio of 4:3 and their monthly expenses are in the ratio of 3 2

Each saves Rs. 6,000 per month.

Now,

Let income be I and expenses be E

Income = 4I : 3I

Expenses = 3E : 2E

4I - 3E = 6000.....(i)

3I - 2E = 6000.....(ii)

Thus by solving the equation (i) and (ii)

I = E = 6000

Therefore, income of X = 4 x 6000 = 24000

Income of Y = 3 x 6000 = 18000

Total income = 24000 + 18000 = 42000

Hence option (b) is correct

Q4. A sum of Rs. 2,500 is distributed among X, Y and Z in the ratio : : : What is the difference between the maximum share and the minimum share? [CSAT 2020]

(a) Rs. 300

(b) Rs. 350

(d) Rs. 450

Solution:

Given that,

A sum of Rs. 2,500 is distributed among X, Y and Z in the ratio : :

Now,

LCM of 2, 4 and 6 = 12

So,

(1/2) x 12 = 6, (3/4) x 12 = 9, (5/6) x 12 = 10

Let X has Rs. 6a

Y has Rs. 9a

Z has Rs. 10a

Thus,

X + Y + Z = 2500

6a + 9a + 10a = 2500

25a = 2500

a = 100

Amount distributed = 600, 900 and 1000

The difference between maximum and minimum amount = 1000 - 600 = Rs. 400

Hence option (c) is correct

Q5. An amount of money was distributed among A, B and C in the ratio p : q : r.

Consider the following statements: [CSAT 2021]

1. A gets the maximum share if p is greater than (q + r).

2. C gets the minimum share if r is less than (p+q).

Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Solution:

Given that,

An amount of money was distributed among A, B and C in the ratio p : q : r

Now,

Share of A = p/(p + q + r)

Share of B = q/(p + q + r)

Share of C = r/(p + q + r)

1. A gets the maximum share if p is greater than (q + r).

If p > q and p > r, then A would get the maximum share.

Hence statement 1 is correct

2. C gets the minimum share if r is less than (p+q).

Let's consider p = 5, q = 6 and r = 8

Though r < p + q but r > p and r > q

Hence statement 2 is incorrect

Q6. A person X wants to distribute some pens among 6 children A, B, C, D, E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number? [CSAT 2022]

(a) 147

(b) 150

(d) 300

Solution:

Given that,

A person X wants to distribute some pens among 6 children A, B, C, D, E and F.

A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F.

Now,

Let A has P number of pens

B = P/2, C = P/3, D = P/4, E = P/5 and F = P/6

LCM of 2, 3, 4, 5 and 6 = 60

Possible values of P = 60, 120, 180...

Taking P = 120

A = 120, B = 60, C = 40, D = 30, E = 24, F = 20

Total pens = 120 + 60 + 40 + 30 + 24 + 20 = 294 pens

Hence option (c) is correct

ANSWER KEY

1. A
2. A
3. B
4. C
5. A
6. C

Download Ratio & Proportion PYQs PDF

✔️ Download the complete set of Ratio & Proportion PYQs (2011-2024) with solutions in PDF format.
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FAQs on Ratio & Proportion for UPSC

1. How many ratio & proportion questions appear in CSAT?

Typically 2-3 questions annually in CSAT Paper II.

2. What are the most common ratio problems?

· Income/expenditure ratios (30%)

· Mixture problems (25%)

· Age ratio problems (20%)

· Partnership ratios (15%)

· Proportion word problems (10%)

3. Any quick calculation tips?

✔️ For three-variable ratios, find common terms
✔️ In mixture problems, quantity of unchanged component remains same
✔️ Always simplify ratios to lowest terms
✔️ Use unitary method for direct proportion

Conclusion

Mastering Ratio & Proportion PYQs can secure you easy marks in CSAT. This page provides:
✅ All PYQs from 2011-2024
✅ PDF with 50+ solved problems
✅ Time-saving calculation methods

For more UPSC resources, visit iassetu.com.

Internal Links:

· UPSC CSAT Quantitative Aptitude Guide

· Percentage Calculation Shortcuts

· Mixture Problems PYQs