Percentage, Profit & Loss MCQs With Answers
Percentages are the backbone of commercial mathematics, and examiners combine them with buying and selling in endless ways. These percentage, profit and loss MCQs cover finding a percentage of a number, reverse percentages, successive increase and decrease, pass marks, cost price and selling price, gain and loss percent, marked price and discount, successive discounts, and the equal-price trick where one item is sold at a profit and another at a loss. They are a staple of PPSC, FPSC, NTS and bank job tests.
Take a scored quiz instead →What is the value of 15% of 200?
• Calculation: (15 / 100) * 200 = 0.15 * 200 = 30.
If 20% of a number is 45, what is 35% of the same number?
20% of the number = 45, so the number = 45 × 100 ÷ 20 = 225.
35% of 225 = 0.35 × 225 = 78.75.
A man spends 25% of his income on rent and 40% of the remainder on food. What percentage of his income is left?
After rent, 75% of the income is left.
He spends 40% of that 75% on food, leaving 60% of 75% = 45% of his income.
A salary of Rs 40,000 is raised by 5% and then by a further 10%. What is the new salary?
After the 5% raise: 40,000 × 1.05 = Rs 42,000.
After the 10% raise: 42,000 × 1.10 = Rs 46,200. (Successive raises are not simply added: 5% + 10% would give Rs 46,000.)
If a store offers 20% discount on 100, what is the price?
• Discount = 0.20 * 100 = 20. Price = 100 - 20 = 80.
A number is first increased by 20% and then decreased by 20%. What is the net change?
Take the number as 100. After a 20% increase it becomes 120; after a 20% decrease it becomes 120 × 0.8 = 96.
96 is 4 less than 100, so there is a net 4% decrease.
Convert 0.25 to percentage:
• Multiply by 100: 0.25 * 100 = 25%.
What is 20% of 500?
0.20 * 500 = 100.
If 15% of x is 45, then x is:
0.15 * x = 45 => x = 300.
If 20% of x is 40, x is:
0.20 * x = 40 => x = 200.
The price of sugar rises by 25%. By what percentage must a family reduce its consumption to keep its spending unchanged?
Reduction % = rise ÷ (100 + rise) × 100.
25 ÷ 125 × 100 = 20%.
Convert 0.75 into a percentage.
0.75 * 100 = 75%.
If 15% of a number is 30, the number is:
0.15 * x = 30 => x = 30 / 0.15 = 200.
What is 50% of 1/2?
0.5 * 0.5 = 0.25.
If a shopkeeper buys at 100 and sells at 120, the profit is:
(20/100) * 100 = 20%.
If 10% of x is 50, then x is:
0.1 * x = 50 => x = 500.
Find 25% of 400.
100.
A man buys an article for Rs. 800 and sells it for Rs. 1000. What is the profit percentage?
(200/800)*100 = 25%.
What is 15% of 600?
0.15 * 600 = 90.
If 25% of x is 50, then x is:
0.25x=50 => x=200.
A shopkeeper marks an item 40% above its cost price and allows a 10% discount. What is his profit percentage?
Take the cost price as 100. Marked price = 140; after a 10% discount, selling price = 140 × 0.9 = 126.
Profit = 126 − 100 = 26, so the profit is 26%.
A shopkeeper sells an item for Rs. 400 and gains 25%. What was the cost price?
1.25 * CP = 400 => CP = 400 / 1.25 = 320.
What is 10% of 200 + 20% of 100?
20 + 20 = 40.
If 50% of x is 200, then x is:
0.5x=200 => x=400.
Find 20% of 1000.
200.
What is 0.5% of 200?
0.005 * 200 = 1.
If a shopkeeper sells an item for 200 at 25% profit, CP is:
1.25x = 200 => x = 160.
What is 15% of 400 + 10% of 200?
60 + 20 = 80.
What is 1/5 as percentage?
0.2 * 100 = 20%.
Find 10% of 500.
50.
A man buys an item for Rs. 500 and sells it for Rs. 600. What is the profit percentage?
(100/500)*100 = 20%.
What is 10% of 10% of 1000?
0.1 * 0.1 * 1000 = 10.
What is 75% of 120?
0.75 * 120 = 90.
If a man sells an item for 150 making a loss of 25%, what was the cost price?
0.75 * CP = 150 => CP = 150/0.75 = 200.
What is 40% of 300 – 20% of 100?
120 - 20 = 100.
If 5% of x is 20, then x is:
0.05x = 20 => x=400.
Find 25% of 80.
20.
What is 20% of 25% of 400?
0.2 * 0.25 * 400 = 0.05 * 400 = 20.
If a shopkeeper sells an item for 120 making 20% profit, the cost price is:
1.2x = 120 => x = 100.
Find 10% of 1000.
100.
A man buys a bicycle for Rs. 2000 and sells it for Rs. 1800. What is the loss percentage?
Loss = 200. Loss% = (200/2000)*100 = 10%.
What is 15% of 600 + 20% of 400?
90 + 80 = 170.
A car is bought for 500k and sold for 600k. What is the profit percentage?
100/500 = 20%.
What is 40% of 250?
0.4 * 250 = 100.
If cost price = 800, loss = 10%, selling price is:
800 - 80 = 720.
Which is 1/4 as a percentage?
0.25 * 100 = 25%.
A man sold a watch for Rs. 400 at a loss of 20%. What was the cost price?
0.8x = 400 => x = 500.
Find the value of 50% of 40% of 1000.
0.5 * 0.4 * 1000 = 200.
If 10% of x is 20, x is:
0.1x = 20.
If 15% of a number is 225, what is 25% of the same number?
0.15x = 225 => x = 1500. 0.25 * 1500 = 375.
In a class, 60% of students passed in Math, 50% in English. 40% passed in both. What % passed in at least one?
60+50-40 = 70.
If 10% discount is given on an item marked Rs. 500, what is the selling price?
500 - 50 = 450.
What is 20% of 400 + 30% of 300?
80 + 90 = 170.
What is 3/4 as a percentage?
0.75 * 100 = 75%.
A man spends 75% of his income and saves Rs. 1500. What is his monthly income?
Savings = 25% = 1500. Income = 1500 * 4 = 6000.
A shopkeeper buys an article for Rs. 200 and sells it for Rs. 250. What is the gain percent?
Gain = 50. Gain % = (50/200)*100 = 25%.
What is 50% of 20% of 500?
0.5 * 0.2 * 500 = 0.1 * 500 = 50.
If 20% of a value is 50, what is the value?
0.2x = 50 => x = 250.
If 20% of a number is 120, what is 120% of that number?
0.2x = 120 => x = 600. 1.2 * 600 = 720.
If 10% of x is 5, what is x?
0.1x = 5 => x = 50.
A merchant sells an item at 10% loss. If he sells for Rs. 50 more, he gains 10%. Find CP.
0.9x + 50 = 1.1x => 0.2x = 50 => x = 250.
CP=300, SP=360. Profit %?
60/300=1/5=20%.
Number + 20% = 120. Number?
1.2x=120 => x=100.
The length and breadth of a rectangle are 12m and 8m. If the length is increased by 25%, find the new area.
Original Area = 96. New Length = 12 * 1.25 = 15. New Area = 15 * 8 = 120.
If 5% of x = 10% of 20, find x.
0.05x = 0.1 * 20 = 2 => x = 40.
A man buys an item for Rs. 500 and sells it for Rs. 400. Find the loss percentage.
Loss = 100. Loss% = (100/500)*100 = 20%.
Marked Price = 600, Discount = 10%. Selling Price?
600 * 0.9 = 540.
A number decreased by 20% is 40. Find the number.
0.8x = 40 => x = 50.
Exam: 40% pass. Student gets 160, fails by 20. Total?
Pass = 180. 180 / 0.4 = 450.
A man sells a chair for Rs. 720, gaining 20%. What was the cost price?
CP * 1.20 = 720 => CP = 720 / 1.2 = 600.
If 40% of a number is 80, what is 100% of the number?
0.4x = 80 => x = 200.
A merchant sells 20% of his stock at 20% profit. At what % profit must he sell the rest to make 25% overall?
Let stock = 100. Overall profit = 125. 20 sold at 1.2*20 = 24. Remaining 80 must sell for 101. Profit = 21/80 = 26.25%.
A man buys 5 articles for the price at which he sells 4. Find his profit %.
Let the cost of 1 article be Re 1. Then 5 articles cost Rs 5, which is also the selling price of 4 articles.
For 4 articles: CP = Rs 4 and SP = Rs 5, so profit = Rs 1 and profit % = 1/4 × 100 = 25%.
Pass 40%. Student gets 100, fails by 20. Total?
120/0.4 = 300.
A man saves 20% of his income. If his income increases by 10% and his savings percentage remains the same, his savings increase by:
Let Income = 100. Saving = 20. New Income = 110. New Saving = 20% of 110 = 22. Increase = (22-20)/20 * 100 = 10%.
If a shopkeeper sells an item for Rs. 450 after a 10% discount, what was the marked price?
Marked Price * (1 - 0.10) = 450 => MP * 0.9 = 450 => MP = 450 / 0.9 = 500.
A person buys an article for Rs. 80 and sells it for Rs. 100. Find the profit percentage.
Profit = 100 - 80 = 20. Profit % = (20/80) * 100 = 25%.
CP = 200, SP = 250. Loss or Gain %?
Profit = 50. 50/200 = 1/4 = 25%.
A number decreased by 10% is 90. Find number.
0.9x = 90 => x = 100.
Passing marks 30%. Student gets 90, fails by 30. Total marks?
Pass = 90 + 30 = 120. 0.3 * M = 120 => M = 400.
A shopkeeper marks an item 20% above the cost price and allows a 10% discount. Find his profit percentage.
Let CP = 100. MP = 120. Selling Price = 120 * 0.9 = 108. Profit = 8%.
If 30% of a number is 60, what is 40% of the number?
0.3x = 60 => x = 200. 0.4 * 200 = 80.
A man buys 5 pens for Rs. 20 and sells 4 pens for Rs. 20. Find his profit percentage.
CP per pen = 4, SP per pen = 5. Profit = 1/4 = 25%.
If an article sold for 500 incurs a 20% loss, what was the CP?
0.8 * CP = 500 => CP = 500 / 0.8 = 625.
A number increased by 25% becomes 125. What is the number?
1.25x = 125 => x = 100.
Exam: 40% to pass. Student gets 140, fails by 20. Total marks?
Pass mark = 160. 0.4 * M = 160 => M = 400.
If 60% of a number is 120, what is 20% of that number?
- Find the number first: 0.6x = 120, so x = 120 ÷ 0.6 = 200.
- Now take 20% of 200, which gives 40.
- Faster route: 20% is one third of 60%, so the answer is simply 120 ÷ 3 = 40.
- Option D 80 is what you get by taking 40% of the number instead of 20%.
- Once you know 10% of the number is 20, every other percentage is just a multiple of that.
A man sells two articles for Rs. 600 each. One at 20% profit and one at 20% loss. What is the total gain or loss?
Loss% = (common_percent/10)^2 = 2^2 = 4% loss.
Gain of 20% on SP is equal to what gain % on CP?
If SP=100, Gain=20, CP=80. Gain% on CP = 20/80 * 100 = 25%.
A number decreased by 20% becomes 80. Find number.
- A 20% decrease leaves 80% of the original number, so the equation is 0.8x = 80.
- Divide to solve: x = 80 ÷ 0.8 = 100.
- Check it: 20% of 100 is 20, and 100 − 20 = 80.
- Adding 20% to 80 gives 96, not 100, because the percentage must be taken from the original number.
- Percentage decrease MCQs in FPSC and PPSC papers follow this same 0.8x pattern, so writing the equation first is the safest step.
Passing marks 33%. A student gets 80, fails by 19. Total marks?
- Failing by 19 marks means the pass mark is 80 + 19 = 99.
- The pass mark is 33% of the total, so 0.33M = 99 and M = 99 ÷ 0.33 = 300.
- Check it: 33% of 300 is 99, and the student's 80 falls 19 short of that.
- The 19 marks are added to the student's score, not subtracted, because the student was below the pass mark.
- Had the question said the student passed by 19, the pass mark would instead be 80 − 19 = 61.
A trader sells an article at a loss of 12%. If he had sold it for Rs. 180 more, he would have gained 8%. Find the cost price of the article.
Difference in percentages = 8% - (-12%) = 20%. 20% of Cost Price = Rs. 180 => Cost Price = (180 / 20) * 100 = Rs. 900.
If A’s salary is 20% less than B’s salary, by what percentage is B’s salary more than A’s salary?
Percentage increase = [R / (100 - R)] * 100 = [20 / 80] * 100 = 25%.
A marked price of a watch is Rs. 1,600. After giving two successive discounts, it is sold for Rs. 1,224. If the first discount is 10%, find the second discount rate.
Price after 1st discount = 1600 * 0.90 = Rs. 1,440. Second discount amount = 1440 - 1224 = Rs. 216. Second discount rate = (216 / 1440) * 100 = 15%.
A person buys 12 items for Rs. 10 and sells 10 items for Rs. 12. Find his profit percentage.
CP of 1 item = 10 / 12 = Rs. 5/6. SP of 1 item = 12 / 10 = Rs. 6/5. Profit % = [(6/5 - 5/6) / (5/6)] * 100 = [(11/30) / (5/6)] * 100 = (11 / 25) * 100 = 44%.
If 75% of a number is added to 75, the result is the number itself. Find the number.
Let number be x. 0.75x + 75 = x => 0.25x = 75 => x = 75 / 0.25 = 300.
A student has to secure 40% marks to pass an exam. He gets 178 marks and fails by 22 marks. What are the maximum marks?
Passing marks = 178 + 22 = 200. 40% of Maximum Marks = 200 => Maximum Marks = 200 / 0.40 = 500.
By selling an item for Rs. 1,440, a trader loses 10%. At what price should he sell it to make a profit of 15%?
Cost Price CP = 1440 / 0.90 = Rs. 1,600. For 15% profit, Selling Price SP = 1600 * 1.15 = Rs. 1,840.
If the price of petrol increases by 25%, by what percentage must a motorist reduce consumption so that expenditure remains unchanged?
Reduction percentage = [R / (100 + R)] * 100 = [25 / 125] * 100 = 20%.
A shopkeeper marks a jacket 40% above cost price and gives a discount of 25%. Find his profit percentage.
Let CP = 100. MP = 140. SP = 140 * (1 - 0.25) = 105. Profit = 105 - 100 = 5%.
A person sells two items at Rs. 990 each, gaining 10% on one and losing 10% on the other. What is his overall gain or loss percentage?
When two items are sold at same price with equal % gain and loss, overall effect is always a loss of (x / 10)^2 % = (10 / 10)^2 % = 1% loss.
If 60% of students in a school are boys and the number of girls is 480, find the total number of students in the school.
Percentage of girls = 100% - 60% = 40%. 40% of Total = 480 => Total = 480 / 0.40 = 1200.
If 20% of a number is added to 80, the result is the number itself. What is the number?
Let number be x. 0.20x + 80 = x => 0.80x = 80 => x = 100.
By selling 33 meters of cloth, a shopkeeper gains the selling price of 11 meters. What is the gain percentage?
Gain = SP of 11 m. SP of 33 m - CP of 33 m = SP of 11 m => CP of 33 m = SP of 22 m. Profit % = (Gain / CP) * 100 = (11 / 22) * 100 = 50%.
If 15% of A is equal to 20% of B, then 25% of A is equal to what percent of B?
0.15 A = 0.20 B => A = (20/15) B = (4/3) B. 25% of A = 0.25 * (4/3) B = (1/3) B = 33.33% of B.
The difference between CP and SP of an article is Rs. 240. If the profit is 20%, find the selling price.
Profit = SP - CP = 240. 20% of CP = 240 => CP = 240 / 0.20 = Rs. 1,200. SP = 1200 + 240 = Rs. 1,440.
A candidate needs 33% marks to pass. He gets 125 marks and fails by 40 marks. What are the maximum marks?
Pass marks = 125 + 40 = 165. 33% of Max Marks = 165 => Max Marks = 165 / 0.33 = 500.
In a class, 60% of students passed in English and 70% passed in Mathematics. If 20% failed in both subjects, what percentage passed in both?
Total students = 100%. Percentage passing in at least one subject = 100% - 20% = 80%. n(E U M) = n(E) + n(M) - n(E n M) => 80 = 60 + 70 - n(E n M) => n(E n M) = 130 - 80 = 50%.
By selling an article for Rs. 720, a trader suffers a loss of 10%. At what price must he sell it to gain 20%?
CP = 720 / 0.90 = Rs. 800. For 20% profit, SP = 800 * 1.20 = Rs. 960.
A radius of a circle is increased by 20%. By what percentage does its area increase?
Area is proportional to r^2. Percentage change = 20 + 20 + (20 * 20)/100 = 40 + 4 = 44%.
By selling a watch for Rs. 1,140, a man loses 5%. At what price should he sell it to gain 5%?
Selling price = Rs. 1,140 at 95% CP => CP = 1140 / 0.95 = Rs. 1,200. To gain 5%, SP = 1200 * 1.05 = Rs. 1,260.
If 35% of a number is 105, what is 80% of that number?
Let the number be x. 0.35 * x = 105 => x = 105 / 0.35 = 300. 80% of 300 = 0.80 * 300 = 240.
A shopkeeper allows a 15% discount on the marked price of an item and still makes a 19% profit. By what percentage is the marked price above CP?
Let CP = 100 => SP = 119. MP * (1 - 0.15) = 119 => 0.85 * MP = 119 => MP = 119 / 0.85 = 140. Marked price is 40% above CP.
If 40% of (A – B) = 20% of (A + B), then B is what percent of A?
0.4(A - B) = 0.2(A + B) => 2(A - B) = A + B => 2A - 2B = A + B => A = 3B => B/A = 1/3 = 33.33%.
A trader marks his goods 25% above cost price and allows a discount of 10%. What is his profit percentage?
Let CP = 100. MP = 125. SP = 125 - (10% of 125) = 125 - 12.5 = 112.5. Profit % = 112.5 - 100 = 12.5%.
If the radius of a sphere is reduced by 50%, by what percentage does its surface area decrease?
Surface area is proportional to r^2. If new r = 0.5r, new area = (0.5)^2 * original area = 0.25 * original area. Decrease = 100% - 25% = 75%.
If 15% of a number is 45, what is 40% of the same number?
Let the number be x. 0.15 * x = 45 => x = 45 / 0.15 = 300. 40% of 300 = 0.40 * 300 = 120.
A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price?
Loss = 15% of 1400 = 0.15 * 1400 = Rs. 210. Selling price = 1400 - 210 = Rs. 1190.
Convert 5/8 into a percentage.
Percentage = (5 / 8) * 100 = 0.625 * 100 = 62.5%.
A shopkeeper marks an item 30% above CP and offers a 10% discount. What is his profit percentage?
Let CP = 100. Marked Price = 130. Discount = 10% of 130 = 13. Selling Price = 130 - 13 = 117. Profit = 17%.
A article is bought for Rs. 450 and sold for Rs. 540. What is the profit percentage?
Profit = 540 - 450 = Rs. 90. Profit % = (90 / 450) * 100 = 20%.
If 20% of a number is equal to 35, what is 60% of that number?
Let the number be x. 0.20 * x = 35 => x = 175. 60% of 175 = 0.60 * 175 = 105.
A shopkeeper gives two successive discounts of 10% and 20%. What is the equivalent single discount?
Equivalent discount = x + y - (xy/100) = 10 + 20 - (10*20/100) = 30 - 2 = 28%.
A trader allows a 15% discount on the marked price of an item. If the marked price is Rs. 1200, what is the selling price?
Discount = 15% of 1200 = 0.15 * 1200 = Rs. 180. Selling Price = 1200 - 180 = Rs. 1020.
In a class of 50 students, 60% are girls. How many boys are in the class?
Percentage of boys = 100% - 60% = 40%. Number of boys = 40% of 50 = 0.40 * 50 = 20.
By selling a bicycle for Rs. 2850, a shopkeeper gains 14%. What was the cost price?
Cost Price = Selling Price / (1 + Profit%) = 2850 / (1 + 0.14) = 2850 / 1.14 = Rs. 2500.
A worker’s salary is increased by 10% and then decreased by 10%. What is the net percentage change?
Net change formula = x + y + (x*y)/100 = 10 - 10 + (10 * -10)/100 = -1%. A 1% decrease.
If x% of 250 is 50, what is the value of x?
(x / 100) * 250 = 50 => 2.5 * x = 50 => x = 50 / 2.5 = 20.
What is the discount percentage if a book marked at Rs. 250 is sold for Rs. 200?
Discount = 250 - 200 = Rs. 50. Discount % = (50 / 250) * 100 = 20%.
By selling a watch for Rs. 450, a man loses 10%. At what price should he sell it to gain 20%?
CP = 450 / 0.90 = Rs. 500. To gain 20%, SP = 500 * 1.20 = Rs. 600.
A article bought for Rs. 800 is sold for Rs. 960. What is the percentage profit?
Profit = Selling Price - Cost Price = 960 - 800 = 160. Profit Percentage = (Profit / Cost Price) * 100 = (160 / 800) * 100 = 20%.
If 40% of a number is 160, what is 65% of that same number?
Let the number be X. 0.40 * X = 160, so X = 160 / 0.40 = 400. Now find 65% of 400: 0.65 * 400 = 260.
By selling an article for Rs. 720, a trader incurs a loss of 10%. What was the cost price?
Selling Price = 0.90 * Cost Price => 720 = 0.90 * CP => CP = 720 / 0.90 = Rs. 800.
In a class of 50 students, 60% passed in English and 50% passed in Math. If 20% passed in both, how many failed in both?
Passed at least one = %Eng + %Math - %Both = 60% + 50% - 20% = 90%. Failed both = 100% - 90% = 10%. 10% of 50 students = 5 students.
Find the value of 15% of 200 + 25% of 120.
15% of 200 = 30. 25% of 120 = 30. Total = 30 + 30 = 60.
A shopkeeper marks an item at Rs. 500 and offers a discount of 15%. What is the selling price?
Discount = 0.15 * 500 = Rs. 75. Selling Price = Marked Price - Discount = 500 - 75 = Rs. 425.
A shopkeeper sells an article for Rs. 480 at a loss of 20%. At what price should he sell it to make a profit of 20%?
Let Cost Price (CP) = X. Selling Price at 20% loss = 0.80X = 480, so X = 480 / 0.80 = Rs. 600. To earn a 20% profit, Selling Price = 1.20 × CP = 1.20 × 600 = Rs. 720.
If 25% of a number is equal to 35% of 150, what is the number?
Let the number be N. 25% of N = 0.25 × N. 35% of 150 = 0.35 × 150 = 52.5. So 0.25 × N = 52.5 => N = 52.5 / 0.25 = 210.
A shopkeeper buys an article for Rs. 400 and sells it for Rs. 500. What is his profit percentage?
Profit = 500 - 400 = Rs. 100. Profit % = (100 / 400) * 100 = 25%.
What is 35% of 240?
35% of 240 = (35 / 100) * 240 = 0.35 * 240 = 84.
By selling an item for Rs. 270, a trader loses 10%. What was the cost price?
Selling Price = CP * (1 - Loss%) => 270 = CP * (1 - 0.10) => 270 = 0.90 * CP => CP = 270 / 0.90 = Rs. 300.
Express 3/8 as a percentage.
Percentage = (3 / 8) * 100 = 300 / 8 = 37.5%.
A man buys a toy for Rs. 25 and sells it for Rs. 30. What is his gain percentage?
Profit = Selling Price (SP) - Cost Price (CP) = 30 - 25 = Rs. 5. Profit Percentage = (Profit / Cost Price) * 100 = (5 / 25) * 100 = 20%.
What percentage of 2 hours is 18 minutes?
Convert hours into minutes: 2 hours = 120 minutes. Required Percentage = (18 / 120) * 100 = 15%.
If the cost price of 10 articles is equal to the selling price of 8 articles, what is the profit percentage?
Let CP of 1 article = Re 1. CP of 8 articles = Rs 8. SP of 8 articles = CP of 10 articles = Rs 10. Profit on 8 articles = 10 - 8 = Rs 2. Profit Percentage = (2 / 8) * 100 = 25%.