Q: In a town, the present number of employed people is 40,000. If the number of employed men decreases by 4% and the number of employed women increases by 12%, the total employed population becomes 40,480. What is the present number of employed men?

27,000. Let men be $m$ and women be $40000-m$. After the changes, total becomes $0.96m + 1.12(40000-m)=40480$. Solving gives $m=27000$.

Q: In an election, 75% of eligible voters participated. Of these, 4% votes were invalid. If a winning candidate got 13,500 votes, which was 55% of the valid votes, what was the total number of eligible voters (to the nearest integer)?

34091. If 13,500 is 55% of valid votes, then valid votes = $13500/0.55$. Since 4% of polled votes were invalid, valid votes are 96% of polled votes. Then polled votes are 75% of eligible voters, so the eligible voters can be found by reversing these percentages.

Q: A company organized training for 120 employees and 15 supervisors. Each employee got a kit with items equal to 12% of the total number of employees. Each supervisor got a kit with items equal to 20% of the total number of employees. How many total kit items were distributed?

2088. Total employees = 120, so each employee kit has $12\%$ of 120 = 14.4 items. Each supervisor kit has $20\%$ of 120 = 24 items. Total items = $120\times14.4 + 15\times24 = 1728 + 360 = 2088$.

Question 1

If 40% of P = 0.5 of Q = $\frac{1}{8}$ of R, find P : Q : R.

Accepted Answer

5: 4: 16. Let $40\%$ of $P = 0.5$ of $Q = \frac{1}{8}$ of $R = x$. Then $P=\frac{x}{0.4}=\frac{5x}{2}$, $Q=\frac{x}{0.5}=2x$, and $R=8x$. So the ratio is $\frac{5}{2}:2:8 = 5:4:16$.

Question 2

Evaluate: $15\frac{1}{3}\%$ of 480 km + $58\frac{1}{3}\%$ of 300 km.

Accepted Answer

248.6 km. $15\frac{1}{3}\% = \frac{23}{150}$, so its value on 480 km is $480	imes\frac{23}{150}=73.6$ km. Also, $58\frac{1}{3}\% = \frac{7}{12}$, so its value on 300 km is $300	imes\frac{7}{12}=175$ km. Adding gives $73.6+175=248.6$ km.

Question 3

A sales agent earns 3% commission on laptops priced at ₹40,000 each and 8% commission on printers priced at ₹8,000 each. If in a week he sells 4 laptops and 10 printers, what is his total commission for 5 such weeks?

Accepted Answer

₹ 56,000. Commission per laptop is 3% of ₹40,000 = ₹1,200, so 4 laptops give ₹4,800. Commission per printer is 8% of ₹8,000 = ₹640, so 10 printers give ₹6,400; weekly total = ₹11,200. For 5 weeks, total commission = ₹11,200 × 5 = ₹56,000.

Question 4

The radius of a circular plate is increased by 8%. What will be the approximate percentage increase in its area?

Accepted Answer

16.64%. The area of a circle is proportional to the square of its radius. If the radius increases by 8%, the new area becomes $(1.08)^2 = 1.1664$ times the original area. So the percentage increase is 16.64%.

Question 5

A family spends on groceries, rent, and other expenses in the ratio 3:5:2. Next year, groceries are expected to rise by 8%, rent by 4%, and other expenses to fall by 10%. What will be the overall percentage change in total expenditure?

Accepted Answer

2.4% increase. Let the original expenditure be 10 units, split as 3, 5, and 2. After the changes, the new expenditure becomes 31.08 + 51.04 + 20.90 = 10.24 units. So the total expenditure increases by 0.24 units, i.e. 2.4%.

Question 6

The budget of a factory is distributed among raw materials, wages, and maintenance in the ratio 4:3:3. During a year, the cost of raw materials rises by 12%, wages by 8%, and maintenance falls by 10%. What is the overall percentage change in the total budget?

Accepted Answer

4.2% increase. Let the original budget be 10 units, split as 4, 3, and 3. After changes, the new cost becomes 4×1.12 + 3×1.08 + 3×0.90 = 10.42 units, so the increase is 0.42 units out of 10, i.e. 4.2%.

Question 7

In a town, the present number of employed people is 40,000. If the number of employed men decreases by 4% and the number of employed women increases by 12%, the total employed population becomes 40,480. What is the present number of employed men?

Accepted Answer

27,000. Let men be $m$ and women be $40000-m$. After the changes, total becomes $0.96m + 1.12(40000-m)=40480$. Solving gives $m=27000$.

Question 8

In an election, 75% of eligible voters participated. Of these, 4% votes were invalid. If a winning candidate got 13,500 votes, which was 55% of the valid votes, what was the total number of eligible voters (to the nearest integer)?

Accepted Answer

34091. If 13,500 is 55% of valid votes, then valid votes = $13500/0.55$. Since 4% of polled votes were invalid, valid votes are 96% of polled votes. Then polled votes are 75% of eligible voters, so the eligible voters can be found by reversing these percentages.

Question 9

A company organized training for 120 employees and 15 supervisors. Each employee got a kit with items equal to 12% of the total number of employees. Each supervisor got a kit with items equal to 20% of the total number of employees. How many total kit items were distributed?

Accepted Answer

2088. Total employees = 120, so each employee kit has $12\%$ of 120 = 14.4 items. Each supervisor kit has $20\%$ of 120 = 24 items. Total items = $120\times14.4 + 15\times24 = 1728 + 360 = 2088$.

Question 10

An item is marked at ₹4,000. A discount offer changes from 12% to 18%. How much extra discount does a customer get?

Accepted Answer

₹ 240. The extra discount is the increase from 12% to 18%, which is 6% of ₹4,000. So the extra discount = 0.06 × 4,000 = ₹240.

Question 11

Evaluate: 75% of 400 - 32.5% of 200 + 18% of 300

Accepted Answer

289. 75% of 400 = 300, 32.5% of 200 = 65, and 18% of 300 = 54. So the value is 300 - 65 + 54 = 289.

Question 12

In an entrance test with 180 questions, there are three sections: Physics (40 questions), Chemistry (70 questions), and Biology (70 questions). A student answered 75% of Physics, 55% of Chemistry, and 45% of Biology questions correctly. If the minimum passing score is 62%, how many more qu

Accepted Answer

11.6. The student got 30 correct in Physics, 38.5 in Chemistry, and 31.5 in Biology, totaling 100 correct answers. Passing requires 62% of 180 = 111.6 correct answers, so the shortfall is 11.6.

Question 13

4.5% of 600 = ?

Accepted Answer

27. 4.5% means $\frac{4.5}{100}$. Multiplying by 600 gives $0.045	imes 600=27$.

Question 14

A washing machine has a marked price of ₹30,000. It is sold after two successive discounts. If the first discount is 18% and the final selling price is ₹21,528, what is the percentage of the second discount?

Accepted Answer

12.5%. After an 18% discount on ₹30,000, the price becomes ₹24,600. The final selling price is ₹21,528, so the second discount is ₹3,072 on ₹24,600, which is 12.5%.

Question 15

Eighty percent of a number is 20 more than three-fifths of that number. Find the number.

Accepted Answer

100. Let the number be $x$. Then $0.8x = \frac{3}{5}x + 20$. Solving gives $0.2x = 20$, so $x = 100$.

Question 16

A sum of money amounts to ₹13,225 in 2 years at 15% compound interest annually. Find the principal.

Accepted Answer

₹10,000. Under compound interest for 2 years at 15% per annum, amount = $P(1.15)^2$. So $13225 = P \times 1.3225$, giving $P = 10000$.

Question 17

In a class of 60 students, 40% are boys. If 75% of the boys passed, how many boys failed?

Accepted Answer

6. 40% of 60 students are boys, so the number of boys is 24. If 75% of them passed, then 25% failed. 25% of 24 is 6, so 6 boys failed.

Question 18

If 30% of $(A + B)$ = 60% of $(A - B)$, then find the ratio $A:B$.

Accepted Answer

3:1. Given 30% of $(A+B)$ equals 60% of $(A-B)$, we get $0.3(A+B)=0.6(A-B)$. Solving this equation gives $A=3B$, so the ratio is $3:1$.

Question 19

The marked price of a microwave is ₹15,000. It is sold after two successive discounts. If the second discount is 10% and the final selling price is ₹10,800, find the first discount percentage.

Accepted Answer

20%. If the second discount is 10%, then the price before the second discount must be ₹10,800 ÷ 0.9 = ₹12,000. This means the first discount reduced ₹15,000 to ₹12,000, i.e. by ₹3,000. So the first discount percentage is 3000/15000 × 100 = 20%.

Question 20

If P is 40% more than Q, and Q is 25% more than R, find the ratio P:R.

Accepted Answer

7:4. If $Q$ is 25% more than $R$, then $Q=1.25R$. If $P$ is 40% more than $Q$, then $P=1.4Q=1.4	imes1.25R=1.75R$. Therefore, $P:R=1.75:1=7:4$.

Question 21

If 20% of $(A + B)$ = 50% of $(A - B)$, then find the ratio $A:B$.

Accepted Answer

7: 3. The equation is $0.2(A+B)=0.5(A-B)$. Simplifying gives $2(A+B)=5(A-B)$, so $2A+2B=5A-5B$, hence $7B=3A$. Therefore, $A:B=7:3$.

Question 22

If 25% of P is equal to 40% of Q, what is the ratio P:Q?

Accepted Answer

8: 5. Given 25% of P = 40% of Q, we have \frac{25}{100}P = \frac{40}{100}Q. This simplifies to 25P = 40Q, or P/Q = 40/25 = 8/5. Hence, the ratio P:Q is 8:5.

Question 23

A watch is listed at ₹1200. After two successive discounts, it is sold for ₹816. If the first discount offered was 20%, what was the second discount percentage?

Accepted Answer

15%. After a 20% discount on ₹1200, the price becomes ₹960. The final price is ₹816, so the second discount is $960-816=144$, which is $144/960=15\%$.

Question 24

If 20% of $P$ = 15% of $Q$ = 12% of $R$, find $P:Q:R$.

Accepted Answer

3: 4: 5. Let the common value be $k$. Then $P=\frac{k}{0.20}$, $Q=\frac{k}{0.15}$, and $R=\frac{k}{0.12}$. This gives $P:Q:R = \frac{1}{0.20}:\frac{1}{0.15}:\frac{1}{0.12} = 5:\frac{20}{3}:\frac{25}{3} = 15:20:25 = 3:4:5$.

Question 25

If 20% of m is equal to 80% of n, what is the ratio m:n?

Accepted Answer

4:1. Given $20\%$ of m = $80\%$ of n, we have $0.2m = 0.8n$. Dividing both sides by 0.2 gives $m = 4n$, so the ratio m:n is 4:1.

Question 26

A number is increased by 25% and then decreased by 25%. What is the net result?

Accepted Answer

6.25% decrease. If the original value is 100, increasing by 25% gives 125. Decreasing 125 by 25% gives 93.75. This is 6.25% less than the original 100, so the net result is a 6.25% decrease.

Question 27

An employee contributes 25% of their salary to charity. From the remaining amount, 20% is allocated to investments. The rest is divided for education and travel in the ratio 5:3. If the expense on travel is ₹9,000, what is the employee's total salary?

Accepted Answer

₹ 40,000. After charity, 75% of the salary remains. Of this, 20% goes to investments, leaving 80% for education and travel. Since travel is 3/8 of that remaining amount and equals ₹9,000, the total salary comes out to ₹40,000.

Question 28

A man spends 75% of his income. His income increases by 20%, but his expenditure remains the same. By what percent do his savings increase?

Accepted Answer

80%. Let the original income be 100. Then expenditure = 75 and savings = 25. New income = 120, expenditure remains 75, so new savings = 45. Increase in savings = 20, which is $20/25\times100=80\%$.

Question 29

Prakash can complete a work in 20 days. In how many days will the work be completed by Rahul, if his efficiency is 25% more than that of Prakash?

Accepted Answer

16 days. Prakash's rate is 1/20 work per day. Rahul's efficiency is 25% more, so his rate is 1.25 × 1/20 = 1/16 work per day. Hence Rahul completes the work in 16 days.

Question 30

A product is originally priced at ₹3,000. A discount of 10% is applied to the original price. After the discount, 10% GST is charged on the discounted price. What is the net amount paid for the product?

Accepted Answer

₹ 2970. A 10% discount on ₹3000 gives ₹2700. Adding 10% GST on ₹2700 gives ₹2970, which is the net amount paid.

Question 31

The population of a town increases by 5% annually. If the current population is 44,100, what was it two years ago (approximately)?

Accepted Answer

40,000. If the population grows by 5% per year, then after two years it becomes multiplied by $1.05^2=1.1025$. So the population two years ago was $44100/1.1025=40000$.

Question 32

Three numbers are such that the second is 120% of the first, and the third is 75% of the second. What is the ratio of the first to the third?

Accepted Answer

10:9. Let the first number be x. Then the second is 120% of x = 1.2x, and the third is 75% of 1.2x = 0.9x. So the ratio of the first to the third is x : 0.9x = 10 : 9.

Question 33

A value was mistakenly decreased by 10% instead of increased by 10%. By what percent is the final result less than the correct value?

Accepted Answer

18.18%. Let the original value be 100. The correct value after a 10% increase is 110, while the mistaken value after a 10% decrease is 90. The shortfall is 20, and as a percentage of the correct value, $20/110 \times 100 = 18.18\%$.

Question 34

The difference between 25% of a number and 15% of the same number is 150. What is the number?

Accepted Answer

1500. Let the number be $x$. Then $25\%$ of $x$ minus $15\%$ of $x$ equals $150$, so $10\%$ of $x=150$. Hence $x=1500$.

Question 35

The value of a car depreciates 15% in the first year, 10% in the second year, and 20% in the third year. If the initial value was Rs. 50,000, what is its value at the end of 3 years?

Accepted Answer

Rs. 30,600. Successive depreciation means the value is reduced step by step. After 1st year: $50000	imes0.85=42500$; after 2nd year: $42500	imes0.90=38250$; after 3rd year: $38250	imes0.80=30600$. Hence the final value is Rs. 30,600.

Question 36

A mixture contains 70% milk. If 40 liters of water is added to the 100-liter mixture, what is the new percentage of milk?

Accepted Answer

50%. Initially, milk = 70% of 100 L = 70 L. After adding 40 L water, total mixture = 140 L while milk remains 70 L. So the new percentage of milk is $\frac{70}{140}\times 100 = 50\%$.

Question 37

A person spends $\frac{3}{5}$ of his income and saves ₹4000. What is his income?

Accepted Answer

₹ 10,000. If a person spends 3/5 of his income, he saves 2/5 of it. Given savings = ₹4000, so 2/5 of income = 4000. Therefore, income = 4000 × 5/2 = ₹10,000.

Question 38

Out of his total monthly income, a man spends 50% on food and household expenses and 20% on rent. The remaining amount is spent on other miscellaneous items. What percentage of his income is spent on these other items?

Accepted Answer

30%. He spends 50% on food and household expenses and 20% on rent, so total spent is 70%. The remaining 30% is spent on miscellaneous items.

Question 39

X's salary is 50% more than Y's. If Y's salary increases by 10% and X's salary increases by k%, then X's new salary becomes 40% more than Y's new salary. What is the approximate value of k?

Accepted Answer

2.67%. Let Y = 100, so X = 150. After increase, Y becomes 110 and X becomes 150(1 + k/100). Given X's new salary is 40% more than Y's new salary, X = 1.4 × 110 = 154. So 150(1 + k/100) = 154, giving k = 2.67% approximately.

Question 40

A value is increased by 30% and then decreased by an unknown percentage to return to the original value. What is the percentage decrease required?

Accepted Answer

23.08%. If the original value is 100, after a 30% increase it becomes 130. Let the required decrease be $x\%$; then $130(1-x/100)=100$. Solving gives $x=23.08\%$.

Question 41

A store announces a festive deal: "Get 30% off on purchases above Rs. 10,000, and an additional Rs. 1,000 off if the total after discount exceeds Rs. 15,000." A customer buys items worth Rs. 25,000. How much does the customer finally pay?

Accepted Answer

Rs. 16,500. On Rs. 25,000, a 30% discount gives Rs. 17,500. Since this amount is still above Rs. 15,000, an additional Rs. 1,000 is deducted. Final payment = Rs. 16,500.

Question 42

The price of an article first increases by 10% and then decreases by 10%. What is the net percentage change?

Accepted Answer

-1%. If the original price is 100, after a 10% increase it becomes 110. A 10% decrease on 110 gives 99, which is 1 less than 100. So the net change is -1%.

Question 43

The price of a product is decreased by $x\%$ and then increased by $x\%$. The final price becomes 10% less than the original. What is the value of $x$ approximately?

Accepted Answer

31.6. After a decrease of $x\%$ and then an increase of $x\%$, the net multiplier is $1-\frac{x^2}{10000}$. Since the final price is 10% less, the multiplier is 0.9. Solving gives $1-\frac{x^2}{10000}=0.9$, so $x^2=1000$ and $x\approx31.6$.

Question 44

A number is increased by 25% and then decreased by 20%. What is the net change in the number?

Accepted Answer

No change. After a 25% increase, the number becomes 1.25 times the original. Then a 20% decrease makes it $1.25 	imes 0.8 = 1$, so the final value is the same as the original.

Question 45

A bag contains 20% red balls, 30% green balls, and the rest blue balls. If there are 80 blue balls, what is the total number of balls?

Accepted Answer

160. Red and green balls together are 50%, so blue balls are the remaining 50%. If 50% corresponds to 80 balls, then 100% corresponds to 160 balls.

Question 46

A candidate attempted 75% of the questions in an exam. He got 80% of the attempted questions correct, and 10% of the unattempted questions were also awarded marks due to grace. If the total number of questions is 200, how many did he get right?

Accepted Answer

125. He attempted 75% of 200 = 150 questions, and 80% of those were correct, so $150 \times 0.8 = 120$. Unattempted questions = 50, and 10% of them got grace marks, so $50 \times 0.1 = 5$. Total right = $120 + 5 = 125$.

Question 47

Find 25% of 40% of 600.

Accepted Answer

60. 40% of 600 is 240. Then 25% of 240 is 60. So the required value is 60.

Question 48

A man spends 75% of his income. Due to inflation, his expenses increase by 20%, and his income increases by 10%. What is the percentage change in his savings?

Accepted Answer

20% decrease. If income is 100, expenses are 75 and savings are 25. After a 10% income increase, income becomes 110; after a 20% expense increase, expenses become 90. New savings = 110 - 90 = 20, which is a 20% decrease from 25.

Question 49

A 30-litre container of pure milk undergoes a 6-litre removal and 6-litre water replacement process, repeated 4 times. Approximately how much original milk remains?

Accepted Answer

$12\frac{36}{125}$ litres. In each operation, the fraction of milk left is $1-\frac{6}{30}=\frac{4}{5}$. After 4 repetitions, remaining milk = $30\left(\frac{4}{5}\right)^4 = 30\cdot\frac{256}{625} = 12.288$ litres, which is $12\frac{36}{125}$ litres.

Question 50

A man spends 70% of his income. His income increases by 10% and his expenditure by 5%. What is the percentage increase in his savings?

Accepted Answer

21.67%. If original income is 100, expenditure is 70 and savings are 30. New income becomes 110 and new expenditure becomes 73.5, so new savings are 36.5. The increase is 6.5 on 30, which is $\frac{6.5}{30}\times 100 = 21.67\%$.

SSC CGL (Prelims) General: Percentage questions with solutions

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