Percentage - word problems

Percent and word problems:

1.                   Ken left a job paying $75,000 per year to accept a sales job paying $45,000 per year plus 15 percent commission. If each of his sales is for $750, what is the least number of sales he must make per year if he is not to lose money because of the change? 
(A)  40      (B)  200     (C) 266     (D)  267      (E)  600 

2.                   In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If rest of the family's income did not change, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
(A) 64%        (B) 68%           (C) 72%       (D) 76%          (E) 80%

3. After paying a 10 percent tax on all income over $3,000, a person had a net income of $12,000. What was the income before taxes?
(A)  $13,300   (B)  $13,000   (C)  $12,900     (D)  $10,000    (E) $9,000

4. A room contains 160 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
(A)  10      (B)  20    (C)  40       (D)  60       (E)  80

5. In a recent election, Geoff received 0.5 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3,571 more votes to win the election, what is the value of x ?
(A) 50           (B) 54       (C) 56        (D) 60           (E) 63

 6. A professional gambler has won 40% of his 25 poker games for the week so far. If, all of a sudden, his luck changes and he began winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?

7. The price of lunch for 15 people was $207 including a 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?
(A)  11.73         (B)  12             (C)  13.8        (D)  14             (E)  15.87

8. Country X taxes each of its citizens an amount equal to 12 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?
(A)  $40,000       (B) $56,000     (C)  $64,000         (D)  $66,667             (E)  $80,000

9. There are twice as many girls as boys in an English class. If 30 % of the girls and 45% of the boys have already handed in their boo reports, what percent of the students have not yet handed in their reports?

10. A union contract specifies a 6 % salary increase plus a $450 bonus for each employee .For a certain employee, this is equivalent to an 8 % salary increase. What was this employee’s salary before the new contract?

(A)  $21,500       (B) $22,500     (C)  $23,500         (D)  $24,300        (E)  $25,000

11. For an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot .If exactly 25 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated?

(A) 12 %        (B)26 %       (C )29 %     (D) 30 %     (E) 60 %

12. One week a certain truck rental had  a total of 20 trucks , all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning,  what is the greatest number of different trucks that could have been rented out during the week?

(A) 18       (B)  16     (C)  12       (D)  8       (E)  4

13. A company accountant estimates that airfares next year for business trips of a thousand miles or less will increase by 20 percent and airfares for all other business trips will increase by 10 percent. This year total airfares for business trips of a thousand miles or less were $ 9,900 and airfare for all other business were 13,000 .According to the accountant’s estimate if the same business trips will be made next year ,how much will be spent for airfares next year?

(A)  $22,930       (B) $26,180     (C)  $26,330         (D)  $26,490        (E)  $29,770

14. In a certain pond, 50 fish were caught , tagged , and returned to the pond .A few days later, 50 fish were caught again , of which 2 were found to have been tagged .If the percent of tagged fish in the second catch approximates the percent of tagged fish in the second catch approximates  the percent of tagged fish in the pond. What is the approximate number of fish in the pond?

(A) 400       (B)  625     (C)  1,250       (D)  2,500       (E)  10,000

15. If 75 percent of a class answered the first question on a certain test correctly , 55 percent answered the second question on the test correctly and , 20 percent answered neither of the questions correctly , what percent answered both correctly ?

(A) 10%        (B) 20%           (C) 30%       (D) 50%          (E) 65%

 16. The contents of a certain box consist of 14 apples and 23 oranges how many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples ?

(A)3       (B)  6     (C)  14       (D)  17       (E) 20

17. Of the 50 researchers in a workgroup, 40 percent will be assigned to team A and the remaining 60 percent to team B. However, 70 percent of the researchers prefer team A and 30 percent prefer team B what is the least possible number of researchers who will NOT be assigned to the team they prefer?

(A) 15       (B)  17     (C)  20       (D)  25       (E) 30

18. A group of store managers must assemble 280 displays for an upcoming sale . If they assemble 25 percent of the displays during the first hour and 40 percent of the remaining displays during the second hour, how many of the displays will NOT have been assembled by the end of the second hour?

(A) 28      (B) 98     (C) 126       (D) 168       (E) 182

19. If 35% of the acreage of a national forest was destroyed in a wild fire, and the remainder regenerates at a rate of 10% a year, after how many years , assuming no further losses , will the forest exceeds its original acreage ?

(A) 10      (B) 8     (C)  5       (D) 4       (E) 3

20. Aloysius spends 50% of his income on rent , utilities ,and insurance , and 20% on food. If he spend 30% of the remainder on videogames and has no other expenditures , what percent of his left after all of the expenditures?

(A) 30%      (B)  21%        (C) 20%            (D) 9%          (E) 0%

21. Adalstein bought a bag of 15 magic beans for $60. One –third of the beans cost $2 each and the rest cost $5 each. If there was a hole in the bag and all of the more expensive beans fell out, the lost beans represented  approximately what percentage of the money Adalstein paid for all of them?

(A) 7%      (B) 13%        (C) 67%               (D) 83%          (E) 88%