Exercise : Time & Work - General Questions
✔ Time & Work -
General Questions
11.
A, B, and C can do a work in 6, 8, and 12 days. They complete it together and get $1,350. What is B's share?
View Answer
Answer: Option B
Explanation:
Explanation:
Wages are split by efficiency: \(1/6 : 1/8 : 1/12 \implies 4 : 3 : 2\). Total parts = 9. B's share = \((3/9) \times 1350 = \)450.
12.
10 men can finish a work in 10 days, while 12 women can finish it in 10 days. If 15 men and 6 women work together, how long will they take?
View Answer
Answer: Option B
Explanation:
Explanation:
10M = 12W \(\implies\) 1M = 1.2W. 15M + 6W = \(15(1.2W) + 6W = 24W\). Since 12W take 10 days, 24W take 5 days.
13.
A can do 1/4 of a work in 10 days and B can do 1/3 of the work in 20 days. How long for both?
View Answer
Answer: Option B
Explanation:
Explanation:
A total = 40 days, B total = 60 days. Combined = \(1/40 + 1/60 = 5/120 = 1/24\). Time = 24 days.
14.
3 men or 5 women can do a work in 12 days. How long for 6 men and 5 women?
View Answer
Answer: Option B
Explanation:
Explanation:
3M = 5W \(\implies\) 6M = 10W. 6M + 5W = 15W. If 5W take 12 days, 15W take 4 days.
15.
A, B, and C can do a work in 10, 12, and 15 days. A leaves after 2 days and B leaves 3 days before completion. Total time?
View Answer
Answer: Option B
Explanation:
Explanation:
Total work = 60. Eff: A=6, B=5, C=4. Let total time be \(x\). \(6(2) + 5(x-3) + 4x = 60 \implies 12 + 5x - 15 + 4x = 60 \implies 9x = 63 \implies x=7\).
16.
Pipe A fills a tank in 10 hours, Pipe B in 15 hours. Pipe C empties it in 20 hours. If all open, how long to fill?
View Answer
Answer: Option B
Explanation:
Explanation:
Net efficiency = \(1/10 + 1/15 - 1/20 = (6+4-3)/60 = 7/60\). Time = \(60/7 = 8.57\) hours.
17.
12 men work 8 hours a day to finish a task in 10 days. How many hours a day must 8 men work to finish it in 12 days?
View Answer
Answer: Option B
Explanation:
Explanation:
\(M_1D_1H_1 = M_2D_2H_2 \implies 12 \times 10 \times 8 = 8 \times 12 \times H_2 \implies H_2 = 10\) hours.
18.
A, B, and C work on alternate days starting with A. A can do it in 10, B in 20, C in 30 days. Total time?
View Answer
Answer: Option C
Explanation:
Explanation:
Total Work = 60. Eff: A=6, B=3, C=2. In 3 days (1 cycle), work = \(6+3+2 = 11\) units. 5 cycles (15 days) = 55 units. Remaining 5 units: A takes \(5/6\) days. Total = \(15 5/6\) days.
19.
If 4 men and 6 women can do a work in 8 days and 3 men and 7 women in 10 days, find 10 women's time.
View Answer
Answer: Option B
Explanation:
Explanation:
\(8(4M + 6W) = 10(3M + 7W) \implies 32M + 48W = 30M + 70W \implies 2M = 22W \implies 1M = 11W\). Total work = \(8(4(11W) + 6W) = 400W\) units. 10 women take \(400 / 10 = 40\) days.
20.
A tank has a leak which empties it in 8 hours. A tap is turned on which admits 6 liters a minute and it now takes 12 hours to empty. Capacity?
View Answer
Answer: Option B
Explanation:
Explanation:
Leak efficiency = \(-1/8\). With tap = \(-1/12\). Tap efficiency = \(-1/12 - (-1/8) = 1/24\) per hour. Tap fills tank in 24 hours. Capacity = \(24 \text{ hours} \times 60 \text{ min} \times 6 \text{ L/min} = 8,640\) liters.