Time and Work Practice Questions

5 questions per page • Detailed step-by-step solutions

Question 16
Medium
If 5 men and 3 boys can reap 23 hectares in 4 days and if 3 men and 2 boys can reap 7 hectares in 2 days, then how many boys must assist 7 men in order that they may reap 45 hectares in 6 days?
A 1 boy
B 3 boys
C 4 boys
D 2 boys
Correct Answer: D

Explanation:

4(5m + 3b) = 23 and 2(3m + 2b) = 7 → 20m + 12b = 23 and 6m + 4b = 7. Multiply the second by 3: 18m + 12b = 21 → 2m = 2 → m = 1, b = 1/4 hectare/day. Need 6(7 + x/4) = 45 → 7 + x/4 = 7.5 → x = 2 boys.
Question 17
Medium
A contractor decided to complete a work in 90 days. He employed 250 men at the beginning and another 150 men after 60 days and completed the work in stipulated time. Had he not employed the additional men, what percent more time he would have taken to finish the work?
A 25%
B 15%
C 20%
D 18%
Correct Answer: C

Explanation:

Total = 250 × 90 + 150 × 30 = 27,000 man-days. 250 men alone need 27,000/250 = 108 days → 18 extra days = 20% of 90.
Question 18
Hard
Ram Lal is a renowned packager of fruits in Varanasi. He packs 70 mangoes or 56 guavas every day working 7 hours a day. His wife also helps him. She packs 30 mangoes or 24 guavas working 6 hours per day. Ram Lal has to pack 3300 mangoes and 2400 guavas with help of his wife. They works alternately, each day 10 hours. His wife started packaging firs day and works every alternate days. Similarly, Ram Lal started his work second day and and worked alternatively till the completion of the work. In how many days the work will finished?
A 80 days
B 90 days
C 84 days
D 88 days
Correct Answer: C

Explanation:

Per hour: Ram Lal 10 mangoes or 8 guavas, wife 5 mangoes or 4 guavas — both pack guavas at 4/5 the mango rate, so 1 guava = 5/4 mango-units. Total = 3300 + 2400 × 5/4 = 6300 mango-units. In 10-hour days: wife 50, Ram Lal 100 → 150 per 2 days → 6300/150 = 42 cycles = 84 days.
Question 19
Medium
Efficiency of A is 50% more than B and B takes 21 days to complete a piece of work. A started the work alone and then B joined with him in 5 days before actual completion of the work. For how many days A worked alone?
A 6 days
B 5 2/3 days
C 5 days
D 4 2/3 days
Correct Answer: B

Explanation:

A = 21/1.5 = 14 days. Work = 42 units: A 3, B 2. Last 5 days together: 25 units. A alone did 17 → 17/3 = 5 2/3 days.
Question 20
Easy
The rates of working of A and B are in the ratio 4 : 5. What is the ratio of the number of days taken by them to finish a job when working separately?
A 4 : 5
B 16 : 25
C 5 : 4
D 25 : 16
Correct Answer: C

Explanation:

Time is inversely proportional to rate. Rates 4 : 5 → times 5 : 4.