UPSC Prelims PYQ › Quantitative Aptitude › Ratio, Proportion & Partnership
Ratio, Proportion & Partnership — UPSC CSAT Paper II Quantitative Aptitude previous year questions
20 free solved previous year questions on Ratio, Proportion & Partnership, papers from 2013 to 2026, drawn from UPSC CSAT, UPSC CDS, covering questions of the kind UPSC asks in CSAT Paper II. Every answer key has been checked again against published sources and solved independently, and each explanation is written fresh.
Read all 20 questions with answers
- #1UPSC CSAT 2026Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x² and x is inversely proportional to z. For z = 7/25, the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?
- A1/7
- B1/5
- C5/7
- D1
Answer: (B) 1/5Explanation
y is directly proportional to x², so y = kx².
x is inversely proportional to z, so x = c/z.
Given z = 7/25 and x = 5: c = 5 × 7/25 = 7/5.
Given x = 5 and y = 50: k = 50 ÷ 25 = 2.
For y = 98: 2x² = 98, x² = 49, x = 7.
Then z = c/x = (7/5) ÷ 7 = 1/5.
Answer: 1/5, option (b).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #2UPSC CSAT 2026The ratio of male to female workers in two companies A and B is 13 : 10 and 7 : 5 respectively. If both the companies have the same number of female workers, then what is the ratio of the total number of workers in A to those in B?
- A24 : 23
- B23 : 24
- C18 : 17
- D27 : 18
Answer: (B) 23 : 24Explanation
Company A: male : female = 13 : 10. Company B: male : female = 7 : 5.
Make the female numbers equal. LCM of 10 and 5 is 10.
B becomes 14 : 10 (multiply 7 : 5 by 2).
A total = 13 + 10 = 23 parts. B total = 14 + 10 = 24 parts.
Ratio A : B = 23 : 24.
Answer: option (b).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #3UPSC CSAT 2026Three partners A, B and C entered into a business. A invested one-third of the capital for one-third duration. B invested one-fourth of the capital for one-fourth duration. C invested the remaining capital for the whole duration. Out of a profit of ₹17,000, how much profit will C get?
- A₹12,000
- B₹10,000
- C₹12,500
- D₹10,750
Answer: (A) ₹12,000Explanation
Profit share depends on capital × time.
A: (1/3) × (1/3) = 1/9.
B: (1/4) × (1/4) = 1/16.
C's capital = 1 – 1/3 – 1/4 = 5/12, for the full time, so 5/12.
Multiply all by 144: A = 16, B = 9, C = 60. Total = 85.
C's profit = 60/85 × 17,000 = 60 × 200 = ₹12,000.
Answer: option (a).Source: UPSC CSAT 2026 Paper II (Set A); answer key checked by independent computation and against UPSC's provisional key
- #4UPSC CSAT 2025In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X to the number of runs scored by Y is equal to ratio of number of runs scored by Y to number of runs scored by Z.Value-I = Runs scored by XValue-II = Runs scored by YValue-III = Runs scored by ZWhich one of the following is correct?
- AValue-I < Value-II < Value-III
- BValue-III < Value-II < Value-I
- CValue-I < Value-III < Value-II
- DCannot be determined due to insufficient data
Answer: (D) Cannot be determined due to insufficient dataExplanation
X : Y = Y : Z means Y^2 = XZ with X + Y + Z = 37. Whole-number solutions are (9,12,16) and (16,12,9).
These give opposite orderings of X and Z, so no single ordering follows.
Answer: option (d).Source: UPSC CSAT 2025 question; answer key checked by independent computation
- #5UPSC CSAT 2024Two persons P and Q enter into a business. P puts Rs 14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P's share is Rs 400 more than Q's share out of the total profit of Rs 2,000, what is the capital contributed by P?
- ARs 30,000
- BRs 26,000
- CRs 24,000
- DRs 20,000
Answer: (A) Rs 30,000Explanation
Shares: P + Q = 2000 and P - Q = 400, so P = 1200, Q = 800; ratio 3 : 2.
Let P's capital be c; then 8c : 10(c - 14000) = 3 : 2.
16c = 30c - 420000, so c = 30,000. Answer: option (a).Source: UPSC CSAT 2024 question; answer key checked by independent computation
- #6UPSC CSAT 2022A person X wants to distribute some pens among six 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?
- A147
- B150
- C294
- D300
Answer: (C) 294Explanation
A = 2B = 3C = 4D = 5E = 6F. Take A = 60k, then B = 30k, C = 20k, D = 15k, E = 12k, F = 10k; total = 147k.
D gets 15k, which is even only if k is even. Smallest k = 2.
Total = 147 x 2 = 294.
Answer: option (c).Source: UPSC CSAT 2022 question; answer key checked by independent computation
- #7UPSC CSAT 2021A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion 5 : 6 : 7 : 8 : 9 : 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks?
- A2
- B3
- C4
- D5
Answer: (B) 3Explanation
Take 100 as maximum per paper. Total = 360 = 45k, so k = 8.
Marks are 40, 48, 56, 64, 72, 80.
Those below 60 are 40, 48 and 56, i.e. three papers.
Answer: option (b).Source: UPSC CSAT 2021 question; answer key checked by independent computation
- #8UPSC CSAT 2021An amount of money was distributed among A, B and C in the ratio p : q : r.Consider the following statements: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?
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Answer: (A) 1 onlyExplanation
Statement 1: if p > q + r, then p exceeds each of q and r, so A has the largest share. True.
Statement 2: take p:q:r = 5:1:2; r < p + q but B, not C, gets the least. False.
Answer: option (a).Source: UPSC CSAT 2021 question; answer key checked by independent computation
- #9UPSC CSAT 2020A sum of Rs. 2,500 is distributed among X, Y and Z in the ratio 1/2 : 3/4 : 5/6. What is the difference between the maximum share and the minimum share?
- ARs.300
- BRs.350
- CRs.400
- DRs.450
Answer: (C) Rs.400Explanation
Multiply by 12: ratio becomes 6 : 9 : 10 (total 25 parts).
One part = 2500/25 = 100, so shares are 600, 900, 1000.
Difference = 1000 - 600 = Rs. 400.
Answer: option (c).Source: UPSC CSAT 2020 question; answer key checked by independent computation
- #10UPSC CSAT 2017P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?
- A3:1:1
- B3:2:4
- C4:3:4
- D3:1:4
Answer: (A) 3:1:1Explanation
Let Q's rate be 1, so P's rate is 3 and P+Q = 4.
R's rate is 4/4 = 1.
Earnings are shared in the ratio of work rates, 3:1:1.
Answer: option (a).Source: UPSC CSAT 2017 question; answer key checked by independent computation
- #11UPSC CSAT 2016In a class, there are 18 very tall boys. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?
- A6
- B12
- C18
- D21
Answer: (B) 12Explanation
Boys = 18 / (3/4) = 24.
Students = 24 / (2/3) = 36.
Girls = 36 - 24 = 12.
Answer: option (b).Source: UPSC CSAT 2016 question; answer key checked by independent computation
- #12UPSC CSAT 2016The total emoluments of two persons are the same, but one gets allowances to the extent of 65% of his basic pay and the other gets allowances to the extent of 80% of his basic pay. The ratio of the basic pay of the former to the basic pay of the latter is:
- A16:13
- B5:4
- C7:5
- D12:11
Answer: (D) 12:11Explanation
Emoluments are 1.65A and 1.80B, set equal.
A : B = 1.80 : 1.65 = 180 : 165 = 12 : 11.
Answer: option (d).Source: UPSC CSAT 2016 question; answer key checked by independent computation
- #13UPSC CSAT 2015An automobile owner reduced his monthly petrol consumption when the prices went up. The price consumption relationship is as follows:Price (in Rs. per litre) | 40 | 50 | 60 | 75Monthly consumption (in litres) | 60 | 48 | 40 | 32If the price goes up to Rs. 80 per litre, his expected consumption (in litres) will be?
- A30
- B28
- C26
- D24
Answer: (A) 30Explanation
Check price x consumption: 40x60 = 50x48 = 60x40 = 75x32 = 2400.
So monthly spend is constant (consumption varies inversely with price).
At Rs. 80 per litre, consumption = 2400 / 80 = 30 litres.
Answer: option (a).Source: UPSC CSAT 2015 question; answer key checked by independent computation
- #14UPSC CSAT 2015The monthly income of Peter and Paul are in the ratio of 4 : 3. Their expenses are in the ratio of 3 : 2. If each saves Rs. 6,000 at the end of the month, their monthly incomes respectively are (in Rs.)
- A24,000 and 18,000
- B28,000 and 21,000
- C32,000 and 24,000
- D34,000 and 26,000
Answer: (A) 24,000 and 18,000Explanation
Let incomes be 4x, 3x and expenses 3y, 2y.
4x - 3y = 6000 and 3x - 2y = 6000; solving gives x = y = 6000.
Incomes: 4 x 6000 = 24,000 and 3 x 6000 = 18,000.
Answer: option (a).Source: UPSC CSAT 2015 question; answer key checked by independent computation
- #15UPSC CSAT 2013In a rare coin collection, there is one gold coin 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
- A90
- B80
- C60
- D50
Answer: (A) 90Explanation
Let non-gold coins be n and gold coins n/3. Then n/3 + 10 = n/2, so n/6 = 10 and n = 60.
Gold coins now = 20 + 10 = 30, so the total is 30 + 60 = 90.
Answer: option (a).Source: UPSC CSAT 2013 question; answer key checked by independent computation
- #16UPSC CDS 2023A, B, C, D and E enter into a business. They invest money in the ratio 2 : 3 : 4 : 5 : 6. However, the time invested by them is in the ratio 6 : 5 : 4 : 3 : 2. If the profit distributed is directly proportional to time and money invested, then who receives the highest amount of profit?
- AC
- BBoth B and D
- CBoth C and D
- DAll get equal profit
Answer: (A) CExplanation
Profit share is proportional to money x time.
Products: 2x6 = 12, 3x5 = 15, 4x4 = 16, 5x3 = 15, 6x2 = 12.
C has the largest product (16).
Answer: option (a).Source: UPSC CDS 2023 question; answer key checked by independent computation
- #17UPSC CDS 2021The incomes of A, B and C are in the ratio 7 : 9 : 12 and their expenditures are in the ratio 8 : 9 : 15. If A's saving is one-fourth of his income, then the ratio of savings of A, B and C is
- A56 : 99 : 69
- B99 : 56 : 69
- C69 : 56 : 99
- D99 : 69 : 56
Answer: (A) 56 : 99 : 69Explanation
Let incomes be 7x, 9x, 12x and expenditures 8y, 9y, 15y.
A saves 7x/4, so A spends 21x/4 = 8y, giving x = 32y/21.
Savings: A = 56y/21, B = 9x - 9y = 99y/21, C = 12x - 15y = 69y/21.
Ratio 56 : 99 : 69.
Answer: option (a).Source: UPSC CDS 2021 question; answer key checked by independent computation
- #18UPSC CDS 2020Three persons start a business with capitals in the ratio 1/3 : 1/4 : 1/5. The first person withdraws half his capital after 4 months. What is his share of profit if the business fetches an annual profit of Rs 96,800?
- ARs 32,000
- BRs 34,500
- CRs 36,000
- DRs 36,800
Answer: (A) Rs 32,000Explanation
Capitals 1/3 : 1/4 : 1/5 = 20 : 15 : 12.
First person: 20 x 4 + 10 x 8 = 160; others: 15 x 12 = 180 and 12 x 12 = 144. Ratio 160:180:144 = 40:45:36.
Share = 96800 x 40/121 = Rs 32,000.
Answer: option (a).Source: UPSC CDS 2020 question; answer key checked by independent computation
- #19UPSC CDS 2020When a ball is allowed to fall, the time it takes to fall any distance varies as the square root of the distance and it takes 4 seconds to fall 78.40 m. How long would it take to fall 122.50 m?
- A5 seconds
- B5.5 seconds
- C6 seconds
- D6.5 seconds
Answer: (A) 5 secondsExplanation
T is proportional to sqrt(D), so T2/4 = sqrt(122.5/78.4) = sqrt(1.5625) = 1.25.
T2 = 5 seconds.
Answer: option (a).Source: UPSC CDS 2020 question; answer key checked by independent computation
- #20UPSC CDS 2020If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/4, then what is the value of abc/def?
- A1/4
- B3/4
- C3/8
- D27/8
Answer: (C) 3/8Explanation
Take f = 1: e = 1/4, d = 3/4, c = 3/8, b = 3/4, a = 1/4.
abc = 9/128 and def = 3/16, so abc/def = 9/128 x 16/3 = 3/8.
Answer: option (c).Source: UPSC CDS 2020 question; answer key checked by independent computation
Want all the Ratio, Proportion & Partnership questions?
109 more questions on this topic, plus mock tests, revision and progress tracking, are in the full practice set. One payment of ₹499.
Get full access – ₹499 Already have a code? Unlock here