Math Quiz: Problems On Time And Work!

1. A father can do a certain job in x hours. His son takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does the father take to do the job?

9

15

20

12

If the father takes x hours to do the job and the son takes twice as long, then the son takes 2x hours to do the job. When they work together, their combined work rate is 1/x + 1/2x = 1/6. Simplifying this equation, we get 3/2x = 1/6. Cross-multiplying, we find that 2x = 18, so x = 9. Therefore, the father takes 9 hours to do the job.

Explanation

If the father takes x hours to do the job and the son takes twice as long, then the son takes 2x hours to do the job. When they work together, their combined work rate is 1/x + 1/2x = 1/6. Simplifying this equation, we get 3/2x = 1/6. Cross-multiplying, we find that 2x = 18, so x = 9. Therefore, the father takes 9 hours to do the job.

2. A school sold drama tickets for 100 each for donating to an orphanage. One member sold 75% of his tickets and had 80 tickets left. How much money did the member collect?

12000

18000

24000

36000

25 % = 80

75% = 240

240 X 100 = 2,40,000

Explanation

25 % = 80

75% = 240

240 X 100 = 2,40,000

3. Shyam can do a job in 20 days, Ram in 30 days and Singhal in 60 days. If Shyam is helped by Ram and Singhal every 3^rd day, how long will it take for them to complete the job?

10

15

20

25

Shyam can complete 1/20th of the job in a day, Ram can complete 1/30th of the job in a day, and Singhal can complete 1/60th of the job in a day. Every 3rd day, Shyam is helped by Ram and Singhal, so the work done on those days is 1/20 + 1/30 + 1/60 = 1/10th of the job. Therefore, in 3 days, they complete 1/10th of the job. To complete the entire job, they will need 3 * 10 = 30 days. However, since they started on the first day, the total time taken will be 30 - 3 = 27 days. Therefore, the correct answer is 15.

Explanation

Shyam can complete 1/20th of the job in a day, Ram can complete 1/30th of the job in a day, and Singhal can complete 1/60th of the job in a day. Every 3rd day, Shyam is helped by Ram and Singhal, so the work done on those days is 1/20 + 1/30 + 1/60 = 1/10th of the job. Therefore, in 3 days, they complete 1/10th of the job. To complete the entire job, they will need 3 * 10 = 30 days. However, since they started on the first day, the total time taken will be 30 - 3 = 27 days. Therefore, the correct answer is 15.

4. Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it?

54

36

18

25

Let the amount of work done by a man in a day be 'm' and the amount of work done by a woman in a day be 'w'. Therefore, 4 men and 3 women will do 4m + 3w amount of work in a day. If 4 men and 3 women complete the entire work in 6 days, they will complete 16th of the work in a day. Hence, 4m + 3w = 16 ----- eqn (1) From statement (2), we know 5 men and 6 women take 4 days to complete the job. i.e., 5 men and 4 women working together will complete 14th of the job in a day. So, 5m + 6w = 14 ----- eqn (2) m = 1/36. w = 1/54. Hence, she will take 54 days to do the entire work.

Explanation

Let the amount of work done by a man in a day be 'm' and the amount of work done by a woman in a day be 'w'. Therefore, 4 men and 3 women will do 4m + 3w amount of work in a day. If 4 men and 3 women complete the entire work in 6 days, they will complete 16th of the work in a day. Hence, 4m + 3w = 16 ----- eqn (1) From statement (2), we know 5 men and 6 women take 4 days to complete the job. i.e., 5 men and 4 women working together will complete 14th of the job in a day. So, 5m + 6w = 14 ----- eqn (2) m = 1/36. w = 1/54. Hence, she will take 54 days to do the entire work.

5. X, Y, and Z contract a work for Rs. 550. Together X and Y are supposed to do 7/11 of the work. How much does Z get?

110

330

200

150

(A + B)'s work = 7/11 So, C's work = 1 - (7/11) = (11 - 7) / 11 = 4/11 Thus, ratio of (A + B) and C's share = (7/11) : (4/11) = 7 : 4 Hence, C's share in a contract of Rs. 550 = Rs. 550 x (4/11) = Rs. 200.

Explanation

(A + B)'s work = 7/11 So, C's work = 1 - (7/11) = (11 - 7) / 11 = 4/11 Thus, ratio of (A + B) and C's share = (7/11) : (4/11) = 7 : 4 Hence, C's share in a contract of Rs. 550 = Rs. 550 x (4/11) = Rs. 200.

6. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?Which one do you like?

32 1/2

37 1/2

17 1/2

35 1/2

Work done by A in 20 days = 80/100 = 8/10 = 4/5 Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1) Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B) Work done by A and B in 1 day = 1/15 ---(2) Work done by B in 1 day = 1/15 – 1/25 = 2/75 => B can complete the work in 75/2 days = 37 ½ days

Explanation

Work done by A in 20 days = 80/100 = 8/10 = 4/5 Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1) Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B) Work done by A and B in 1 day = 1/15 ---(2) Work done by B in 1 day = 1/15 – 1/25 = 2/75 => B can complete the work in 75/2 days = 37 ½ days

7. P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they complete the job in 4 days. How many days does it take for R alone to complete the work?

9 2/5

9 1/5

9 3/5

None of these

Amount of work P can do in 1 day = 1/16 Amount of work Q can do in 1 day = 1/12 Amount of work P, Q and R can together do in 1 day = 1/4 Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48 => Hence R can do the job on 48/5 days = 9 (3/5) days

Explanation

Amount of work P can do in 1 day = 1/16 Amount of work Q can do in 1 day = 1/12 Amount of work P, Q and R can together do in 1 day = 1/4 Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48 => Hence R can do the job on 48/5 days = 9 (3/5) days

8. A shepherd has 1 million sheep at the beginning of the Year 2000. The numbers grow by x% (x > 0) during the year. A famine hits his village in the next year and many of his sheep die. The sheep population decreases by y% during 2001 and at the beginning of 2002, the shepherd finds that he is left with 1 million sheep. Which of the following is correct?

X > y

Y > x

X = y

Cannot be determined

Let us assume the value of x to be 10%. Therefore, the number of sheep in the herd at the beginning of year 2001 (end of 2000) will be 1 million + 10% of 1 million = 1.1 million In 2001, the numbers decrease by y% and at the end of the year the number sheep in the herd = 1 million. i.e., 0.1 million sheep have died in 2001. In terms of the percentage of the number of sheep alive at the beginning of 2001, it will be (0.1/1.1)*100 % = 9.09%. From the above illustration it is clear that x > y.

Explanation

Let us assume the value of x to be 10%. Therefore, the number of sheep in the herd at the beginning of year 2001 (end of 2000) will be 1 million + 10% of 1 million = 1.1 million In 2001, the numbers decrease by y% and at the end of the year the number sheep in the herd = 1 million. i.e., 0.1 million sheep have died in 2001. In terms of the percentage of the number of sheep alive at the beginning of 2001, it will be (0.1/1.1)*100 % = 9.09%. From the above illustration it is clear that x > y.

9. Tina, Mina, Gina, Lina and Bina are 5 sisters, aged in that order, with Tina being the eldest. Each of them had to carry a bucket of water from a well to their house. Their buckets' capacities were proportional to their ages. While returning, equal amount of water got splashed out of their buckets. Who lost maximum amount of water as a percentage of the bucket capacity?

Bina

Tina

Gina

Lina

Tina is the older and Bina is the youngest. So, Bina's bucket would have been the smallest. Each sister lost an equal amount of water. As a proportion of the capacity of their buckets, Bina would have lost the most.

Explanation

Tina is the older and Bina is the youngest. So, Bina's bucket would have been the smallest. Each sister lost an equal amount of water. As a proportion of the capacity of their buckets, Bina would have lost the most.

10. P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?

8/15

7/15

9/15

6/15

Amount of work P can do in 1 day = 1/15 Amount of work Q can do in 1 day = 1/20 Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60 Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15 Fraction of work left = 1 – 7/15= 8/15

Explanation

Amount of work P can do in 1 day = 1/15 Amount of work Q can do in 1 day = 1/20 Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60 Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15 Fraction of work left = 1 – 7/15= 8/15

11. A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?

20

17

23

21

Let the number of apples be 100. On the first day he sells 60% apples ie.,60 apples. Remaining apples =40. He throws 15% of the remaining i.e., 15% of 40 = 6.Now he has 40 - 6 = 34 apples The next day he throws 50% of the remaining 34 apples i.e., 17. Therefore, in all, he throws 6 + 17 =23 apples.

Explanation

Let the number of apples be 100. On the first day he sells 60% apples ie.,60 apples. Remaining apples =40. He throws 15% of the remaining i.e., 15% of 40 = 6.Now he has 40 - 6 = 34 apples The next day he throws 50% of the remaining 34 apples i.e., 17. Therefore, in all, he throws 6 + 17 =23 apples.

12. If S is 150 percent of T, then T is what percent of S + T?

20%

25%

40%

10%

The easiest way to solve this question is by assuming a value for T. Take T to be 100. Therefore, S = 150% of T = 150% of 100 = 150. So, S + T = 150 + 100 = 250. We need to find out T as a percent of S + T i.e., (100/250) * 100 = 40%

Explanation

The easiest way to solve this question is by assuming a value for T. Take T to be 100. Therefore, S = 150% of T = 150% of 100 = 150. So, S + T = 150 + 100 = 250. We need to find out T as a percent of S + T i.e., (100/250) * 100 = 40%

13. When processing flower - nectar into honeybees' extract, a considerable amount of water gets reduced. How much flower - nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 15% water?

1.5 Kg

1.7 Kg

1.25 Kg

2 Kg

Flower-nectar contains 50% of non-water part. In honey this non-water part constitutes 85% (100-15). Therefore, 0.5 X Amount of flower-nectar = 0.85 X Amount of honey = 0.85 X 1 kg Therefore, amount of flower-nectar needed = (0.85/0.5) * 1kg = 1.7 kg.

Explanation

Flower-nectar contains 50% of non-water part. In honey this non-water part constitutes 85% (100-15). Therefore, 0.5 X Amount of flower-nectar = 0.85 X Amount of honey = 0.85 X 1 kg Therefore, amount of flower-nectar needed = (0.85/0.5) * 1kg = 1.7 kg.

14. In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes and there are no invalid votes, by how many votes did it lose the election?

36000

48000

24000

15000

Let the percentage of the total votes secured by Party D be x% Then the percentage of total votes secured by Party R = (x - 12)% As there are only two parties contesting in the election, the sum total of the votes secured by the two parties should total up to 100% i.e., x + x - 12 = 100 2x - 12 = 100 or 2x = 112 or x = 56%. If Party D got 56% of the votes, then Party got (56 - 12) = 44% of the total votes. 44% of the total votes = 132,000 i.e.,44/100*T = 132,000 T = 132000*100/44 = 300,000 votes. The margin by which Party R lost the election = 12% of the total votes = 12% of 300,000 = 36,000.

Explanation

Let the percentage of the total votes secured by Party D be x% Then the percentage of total votes secured by Party R = (x - 12)% As there are only two parties contesting in the election, the sum total of the votes secured by the two parties should total up to 100% i.e., x + x - 12 = 100 2x - 12 = 100 or 2x = 112 or x = 56%. If Party D got 56% of the votes, then Party got (56 - 12) = 44% of the total votes. 44% of the total votes = 132,000 i.e.,44/100*T = 132,000 T = 132000*100/44 = 300,000 votes. The margin by which Party R lost the election = 12% of the total votes = 12% of 300,000 = 36,000.

15. Two pipes A and B can fill a cistern in 37 1/ 2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour , if the B is turned off after…

5 min

8 min

7 min

9 min

LCM of (75/2 and 45) = 225, assume this is total unit of work. Thus, efficiency of A = [(225)/(75/2)] = 6 units/min and B = 225/45 = 5 units/min. Since A works for 30 mins, he will finish = 6 x 30 = 180 units. Remaining = 225 - 180 = 45 units to be completed by B in = (45/5) = 9 mins.

Explanation

LCM of (75/2 and 45) = 225, assume this is total unit of work. Thus, efficiency of A = [(225)/(75/2)] = 6 units/min and B = 225/45 = 5 units/min. Since A works for 30 mins, he will finish = 6 x 30 = 180 units. Remaining = 225 - 180 = 45 units to be completed by B in = (45/5) = 9 mins.