Practice UPSC CSAT previous year questions from 2011–2026 classified underPercentage. Review the original question, four options, correct answer and explanation for every PYQ.
32 questions • 2011–2026
A person saves 10% of his salary every month. If his salary increases by 12% and the expenditure increases by 10%, then what will be the change in his saving per month?
Take salary 100 and expenditure 90, so saving is 10. New salary=112 and expenditure=99, so saving=13. Increase is 3 on a base of 10, i.e. 30%. Hence B.
An alloy P contains 20% copper and 80% zinc by weight. Another alloy Q contains 60% copper and 40% zinc by weight. A third alloy R is to be prepared from P and Q so that it contains equal amount of copper and zinc. In what ratio, amounts of P and Q be mixed in order to get R?
To reach 50% copper from 20% and 60%, the alligation ratio P:Q=(60−50):(50−20)=10:30=1:3. Hence A.
The price (p) of a commodity is first increased by k%; then decreased by k%; again increased by k%; and again decreased by k%. If the new price is q, then what is the relation between p and q?
Multiplying the four percentage factors gives q=p(10^4−k²)^2/10^8.
The petrol price shot up by 10% as a result of the hike in crude oil prices. The price of petrol before the hike was ₹90 per litre. A person travels 2200 km every month and his car gives a mileage of 16 km per litre. By how many km should he reduce his travel if he wants to maintain his expenditure at the previous level?
The price becomes ₹99; maintaining expenditure reduces distance from 2200 to 2000 km, a reduction of 200 km.
What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey?
Take 100 units of honey. To sell the mixture at the honey's cost price while gaining 20%, add water equal to 20 units of honey. Thus water is 20% of the honey quantity.
P's salary is 20% lower than Q's salary which is 20% lower than R's salary. By how much percent is R's salary more than P's salary?
Let R=100. Then Q=80 and P=64. R exceeds P by 36 on a base of 64: 36/64×100 = 56.25%.
A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake?
For value n, the correct result is 4n and the mistaken result is n/4. The reduction relative to the correct result is (4n−n/4)/(4n)×100 = 93.75%.
In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?
85% passed at least one subject because 15% failed both. English-only plus Hindi-only = (80+70)−2×65 = 20%, equivalently the failed-in-only-one group is 20%.
A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded annually with S% annual rate of interest, which is correct?
For equal effective returns, S=R+R²/400, so S>R.
The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?
Take the original price as 100. After +25% it is 125; after -20% it is 100; after +10% it is 110. The net increase is 10%.
Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list?
X's margin is 56%-44%=12% of votes cast. Thus 0.12 x (0.80N)=1440, so 0.096N=1440 and N=15000.
From January 1, 2021, the price of petrol (in Rupees per litre) on mth day of the year is 80 + 0.1m, where m = 1, 2, 3, …, 100 and thereafter remains constant. On the other hand, the price of diesel (in Rupees per litre) on nth day of 2021 is 69 + 0.15n for any n. On which date in the year 2021 are the prices of these two fuels equal?
After day 100 petrol remains at Rs.90. Diesel reaches Rs.90 when 69+0.15n=90, giving n=140, which is 20 May 2021.
In a class, 60% of students are from India and 50% of the students are girls. If 30% of the Indian students are girls, then what percentage of foreign students are boys?
Take 100 students: 60 Indian, of whom 18 are girls. There are 50 girls total, so 32 foreign girls and 8 foreign boys among 40 foreigners; 8/40=20%.
A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 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?
Taking each paper as 100 marks, total obtained is 360. The common multiplier is 8, giving 40, 48, 56, 64, 72, 80. Three scores are below 60.
In a group of 120 persons, 80 are Indians and rest are foreigners. Further, 70 persons in the group can speak English. The number of Indians who can speak English is
There are 40 foreigners. Even if all 40 foreigners speak English, at least 30 of the 70 English speakers are Indian; therefore the number is at least 30.
Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct?
If 80% are under 25 while 33⅓% are literate, at least some of the literate villagers must be under 25.
P scored 40 marks more than Q in an examination. If Q scored 10% less marks than P, then how much did Q score?
Q=90% of P and P=Q+40. Thus Q=0.9(Q+40), giving Q=360.
In an objective type test of 90 questions, 5 marks are allotted for every correct answer and 2 marks are deducted for every wrong answer. After attempting all the 90 questions, a student got a total of 387 marks. What is the number of incorrect responses?
Maximum is 450. Each wrong answer reduces the score by 7 relative to a correct answer, so 450−387=63=7×9; hence 9 incorrect.
If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price?
Starting from 100, a 20% decrease gives 80 and a 25% increase gives 100, so there is no net change.
A person bought a car and sold it for Rs. 3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car?
Selling price is 80% of cost price. Thus cost price = 3,00,000/0.8 = Rs. 3,75,000.
A shop owner offers the following discount options on an article to a customer: 1. Successive discounts of 10% and 20%, and then pay a service tax of 10%. 2. Successive discounts of 20% and 10%, and then pay a service tax of 10%. 3. Pay a service tax of 10% first, then successive discounts of 20% and 10%. Which one of the following is correct?
The same multiplicative factors 0.9, 0.8 and 1.1 are applied in different orders; multiplication is commutative, so all three give the same final amount.
In adult population of a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers?
If men=M and women=W, 0.4M=0.3W. The married population is 0.8M out of total 7M/3, giving 34 2/7%.
As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for Rs. 1,200. What was the original price of rice per kg?
If original price is p, 1200/p−1200/(1.25p)=6; solving gives p=40.
Anita's mathematics test had 70 problems carrying equal marks i.e., 10 arithmetic, 30 algebra and 30 geometry. Although she answered 70% of the arithmetic, 40% of the algebra and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% marks. The number of more questions she would have to answer correctly to earn a 60% passing marks is:
Correct answers are 7 arithmetic + 12 algebra + 18 geometry = 37. A 60% score on 70 equal-mark questions requires 42 correct, so 5 more are needed.
The monthly average salary paid to all the employees of a company was Rs. 5000. The monthly average salary paid to male and female employees was Rs. 5200 and Rs. 4200 respectively. Then the percentage of males employed in the company is:
Let the male fraction be m. Then 5200m+4200(1−m)=5000, giving 1000m=800 and m=0.8, or 80%.
Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X?
Let Z=100. Then X=80 and Y=72. Y is 8 less than X; 8/80×100=10%.
In a test, a candidate attempted only 8 questions and secured 50% marks in each of the questions. If he obtained a total of 40% in the test and all questions in the test carried equal marks, how many questions were there in the test?
The candidate earned 8×50%=4 question-equivalents. This is 40% of the total, so total questions = 4/0.40 = 10.
Candidates in a competitive examination consisted of 60% men and 40% women. 70% men and 75% women cleared the qualifying test and entered the final test where 80% men and 70% women were successful. Which of the following statements is correct?
Using 100 candidates, 60 men yield 42 qualifiers and 33.6 final successes; 40 women yield 30 qualifiers and 21 final successes. More men succeed in absolute number.
A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden
New area = 1.4 × 0.8 = 1.12 of the old area, so the increase is 12%.
A and B decide to travel from place X to place Y by bus. A has Rs. 10 with him and he finds that it is 80% of the bus fare for two persons. B finds that he has Rs. 3 with him and hands it over to A. In this context, which one of the following statements is correct?
₹10 is 80% of the two-person fare, so the fare is ₹12.50. After B gives ₹3, A has ₹13, leaving ₹0.50 after purchase.
As per agreement with a bank, a businessman had to refund a loan in some equal instalments without interest. After paying 18 instalments he found that 60 percent of his loan was refunded. How many instalments were there in the agreement?
If 18 instalments equal 60%, the total number is 18/0.6 = 30.
In a group of persons, 70% of the persons are male and 30% of the persons are married. If two-sevenths of the males are married, what fraction of the females is single?
Take 100 people: 70 male, so 30 female. Married males = 70×2/7=20; total married =30, so 10 females are married and 20 of 30 females are single = 2/3.
Attempt questions one by one with UPSC-style marking and immediate explanations.