Word Problems
(Fractions & Percents)
Practice Exercise
Very Easy (Difficulty Level-1):
1. 48 of the 60 seats on a bus were occupied, what percent of the seats were not occupied?
(a) 12%
(b) 20%
(c) 25%
(d) 60%
(e) 80%
2. Four people shared a taxi on the airport. The fare was $36.00, and they gave the driver a tip equal to 25 percent of the fare. If they equally shared the cost of the fare and tip, how much did each person pay?
(a) $9.00
(b) $9.75
(c) $10.25
(d) $10.75
(e) $11.25
3. If 60 percent of w equals 20 percent of t. What percent of t is w?
(a) 33.33%
(b) 133.67%
(c) 60%
(d) 120%
(e) 12%
4. 36 percent of 18 is 18 percent of what number?
(a) 9
(b) 24
(c) 36
(d) 40
(e) 48
5. A closer contains 24 pairs of shoes, if 25 percent of those pairs of shoes are black, how many pairs are not black?
(a) 4
(b) 6
(c) 12
(d) 18
(e) 20
6. If 65 percent of x is 195, what is 75 percent of x?
(a) 215
(b) 225
(c) 235
(d) 250
(e) 260
Easy (Difficulty Level-2):
7. What is the percent discount on a jacket marked down from $120 to $100?
(a) 13.33%
(b) 16.67%
(c) 20%
(d) 30%
(e) 40%
8. A survey found that 80 percent of the apartments in city G have smoke alarms installed; of these 20 percent have smoke alarms that are not working. What percent of the apartments in city G were found to have working smoke alarms?
(a) 60%
(b) 64%
(c) 66 %
(d) 70%
(e) 72%
9. A 25-ounces solution is 20 percent alcohol. If 50 ounces of water are added to it what percent of the new solution is alcohol?
(a) 5%
(b) 6 ⅔%
(c) 10%
(d) 13⅓%
(e) 20%
10. The price of a newspaper rises from 5 cents to 15 cents. What is the percent increase in price?
(a) 50%
(b) 75%
(c) 100%
(d) 150%
(e) 200%
11. A Stock decreases in value by 50 percent, by what percent must the stock price increase to reach its former?
(a) 10%
(b) 25%
(c) 50%
(d) 75%
(e) 100%
12. The average home price in Newyork was $260,000 in 2008. If the average price of the home rose by 5% from 2008 to 2009 and then fell from 2009 to 2010 by 10%, what was the average home price in 2010?
Medium (Difficulty Level-3):
13. Of a certain high school graduating class, 75 percent of the students continued their formal education, and 80 percent of those who continued their formal education went to four-year colleges. If 300 students in the class went to four-year colleges, how many students were in the graduating class?
14. If x = 80%, by what percent is x larger than x2?
15. If a ticket increased in price by 20%, and then increased again by 5%, by what percent did the ticket price increase in total?
16. If an index increases by 15% and then falls by 15%, will it return to its original value?
17. In July the price of a stock increased by 10 percent. In August, it declined by 20 percent. If in September the price increased 10 percent, by what percentage of the original July price has the stock changed in price from the start of July to the end of September?
18. Which of the following is 850 percent greater than 8 × 103?
(A) 8.5 × 103
(B) 6.4 × 104
(C) 6.8 × 104
(D) 7.6 × 104
(E) 1.6 × 105
Hard (Difficulty Level-4):
19. By what percent did the price of a book increase if the ratio of the book’s original price to its new price is 4:5.
20. By what percent did the price of a book increase if the ratio of the change in the book’s price to its new price is 1:5.
21. A tour group of 25 people paid a total of $630 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
A. $22
B. $23.94
C. $24
D. $25.20
E. $30
22. If a dealer had sold a stereo for $600, he would have made a 20% profit. Instead, the dealer sold it for a 40% loss. At what price was the stereo sold?
23. A butcher buys 240 kilograms of beef for $380. If 20 percent of the beef is unusable, at approximately what average price per kilogram must he sell the rest of the beef in order to make a profit of 25 percent?
24. If y is 80 percent greater than x, then x is approximately what percent less than y?
Very Hard & Tricky (Difficulty Level-5):
25. During an auction, Jerome sold 75% of the first 1,000 items he offered for sale, and 30% of his remaining items. If he sold 40% of the total number of items he offered for sale, how many items did Jerome offer for sale?
26. Boomtown urban planners expect the city’s population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Whhat is the percent population increase in Boomtown over the last year? (Answer to nearest 0.1 of fraction)
27. At the moment there are 54,210 tagged birds in a certain wildlife refuge. If exactly 20 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?
28. Captown is the capital city of Maltania. If the population of Captown is 25 percent of the rest of the population of Maltania, then the population of Captown is what percent of the entire population of Maltania?
29. If the retail price of a shirt is R dollars, and the price including sales tax is T dollars then the sales tax, as a percent, is?
30. If John has $100 to spend and was unable to buy a particular item before the price was reduced by 60%, but can afford the item after the price reduction, what was the maximum possible price of the item prior to the price reduction?
Answer Sheet:
1. B
2. E
3. A
4. C
5. D
6. B
7. B
8. B
9. B
10. E
11. E
12. $245700
13. 500
14. 25%
15. 26%
16. No
17. Decreased by 3.2%
18. D
19. 25%
20. 25%
21. C
22. $300
23. $2.5
24. 44.4%
25. 4500
26. 65.3%
27. 37.5%
28. 20%
29. 100(T – R)⁄R
30. $250