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1.
A and B together can do a job in 12 days. A works on it for 4 days and then B alone finishes the rest in 18 days. B alone can do the whole job in:
Correct Answer: C [21 days]
Explanation:
4 days of A + 18 of B = 4 days of (A + B) + 14 of B → 14 days of B = 1 − 1/3 = 2/3 → B = 21 days.
2.
10 men can finish a job in 12 days, and 15 women can finish it in 16 days. In how many days will 5 men and 6 women finish it?
Correct Answer: A [15 days]
Explanation:
1 man = 1/120, 1 woman = 1/240 per day → 5/120 + 6/240 = 16/240 = 1/15 → 15 days.
3.
Pipes A and B can fill a tank in 20 and 30 minutes; pipe C can empty it in 15 minutes. A and B are opened together in the empty tank, and after 6 minutes C is also opened. In how many minutes in all is the tank full?
Correct Answer: E [36 minutes]
Explanation:
LCM 60: A 3, B 2, C −4. 6 min → 30 units; then net 1 unit/min → 30 more minutes; total 36.
4.
A is three times as efficient as B and takes 40 days less than B to finish a job. In how many days can they finish it together?
Correct Answer: B [15 days]
Explanation:
Times 1 : 3 → difference 2 parts = 40 → A 20, B 60 → 20 × 60/80 = 15 days.
5.
A can do a job in 20 days and B in 30 days. They start together, but A leaves 5 days before the job is finished. The job is finished in:
Correct Answer: D [15 days]
Explanation:
LCM 60: 3(T − 5) + 2T = 60 → 5T = 75 → T = 15 days.
6.
A can do a job in 6 days and B in 8 days. With the help of C they finish it in 3 days and are paid ₹ 3,200. C's share is:
Correct Answer: C [₹ 400]
Explanation:
In 3 days A does 1/2, B 3/8, so C did 1/8 → 1/8 × 3,200 = ₹ 400.
7.
12 men can complete a job in 18 days. After they have worked for 6 days, 4 more men join them. In how many more days is the job finished?
Correct Answer: A [9 days]
Explanation:
Total 216 man-days; done 72; remaining 144 ÷ 16 men = 9 days.
8.
A and B can do a job in 18 days, B and C in 24 days, and A and C in 36 days. How many days will C alone take?
Correct Answer: B [144 days]
Explanation:
LCM 72: pairs 4, 3, 2 → all three 9/2 = 4.5 units/day; C = 4.5 − 4 (A + B) = 0.5 → 144 days.
9.
Spot My Mistake: "A fills a tank in 10 h, B in 15 h, and a leak empties it in 30 h. (1) LCM = 30 units. (2) A = 3, B = 2, leak = 1 unit/h. (3) Net = 3 + 2 + 1 = 6 units/h. (4) Time = 30 ÷ 6 = 5 h." Which step is wrong, and what is the correct time?
Correct Answer: C [Step (3); 7.5 h]
Explanation:
The leak must be subtracted: 3 + 2 − 1 = 4 units/h → 30 ÷ 4 = 7.5 h.
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