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1.  
A, B and C can do a job in 20, 30 and 60 days respectively. Working together, they finish it in:

Correct Answer: A [10 days]

Explanation:

LCM 60: 3 + 2 + 1 = 6 units/day → 10 days.

2.  
A and B can do a job in 8 days, B and C in 12 days, and C and A in 24 days. In how many days can A, B and C together do it?

Correct Answer: E [8 days]

Explanation:

LCM 24: pairs 3 + 2 + 1 = 6 = 2(A + B + C) → 3 units/day → 8 days.

3.  
15 men working 8 hours a day lay 1.2 km of road in 16 days. In how many days will 20 men working 6 hours a day lay 1.5 km?

Correct Answer: B [20 days]

Explanation:

D₂ = 15 × 16 × 8 × 1.5/(1.2 × 20 × 6) = 2,880/144 = 20.

4.  
A is 60% more efficient than B. Together they finish a job in 20 days. How many days will B alone take?

Correct Answer: C [52 days]

Explanation:

A : B = 8 : 5; work = 13 × 20 = 260 units → B = 260 ÷ 5 = 52 days.

5.  
A can do a job in 12 days and B in 18 days. They do it together and receive ₹ 6,000. A's share is:

Correct Answer: D [₹ 3,600]

Explanation:

LCM 36: efficiency 3 : 2 → A gets 3/5 × 6,000 = ₹ 3,600.

6.  
A pipe can fill a tank in 6 hours. Because of a leak it takes 8 hours. The leak alone can empty the full tank in:

Correct Answer: C [24 hours]

Explanation:

6 × 8/(8 − 6) = 24 hours.

7.  
A can finish a job in 20 days. He works alone for 5 days, and then B, who can finish the job alone in 30 days, joins him. In how many days in all is the job finished?

Correct Answer: E [14 days]

Explanation:

LCM 60: A 3, B 2. 5 days → 15 units; 45 ÷ 5 = 9 more days → 14 days.

8.  
A can do a job in 6 days and B in 9 days. They work on alternate days with A starting. The job is finished in:

Correct Answer: A [7 days]

Explanation:

LCM 18: A 3, B 2; cycle 5 units in 2 days; 3 cycles = 15 units in 6 days; A does the last 3 units on day 7.

9.  
Quantity I: Days taken by 6 men to finish a job that 9 men finish in 14 days.
Quantity II: Days taken by A and B together, if A alone needs 30 days and B alone 70 days.

Correct Answer: E [Quantity I = Quantity II or relation cannot be established]

Explanation:

I: 9 × 14/6 = 21. II: 30 × 70/100 = 21.

10.  
In how many days can B alone finish the job?
I. A and B together finish it in 8 days.
II. A is twice as efficient as B.

Correct Answer: D [Both statements together are needed]

Explanation:

I alone gives only the total; II alone gives only a ratio.

11.  
Trick Spotter: A alone takes 18 days and A and B together take 12 days. Which is the fastest correct way to find B's time alone?

Correct Answer: C [18 × 12/(18 − 12)]

Explanation:

Missing Partner: aT/(a − T) = 216/6 = 36 days.

12.  
Pipe A fills a tank in 4 hours; pipe B empties it in 6 hours. Which of the following is/are correct?
I. If both are opened in the empty tank, it fills in 12 hours.
II. With both open, 1/10 of the tank fills in 1 hour.
III. If both are open for 6 hours and then B is closed, A fills the rest in 2 hours.

Correct Answer: C [Only I and III]

Explanation:

Net 1/4 − 1/6 = 1/12 per hour: I true, II false; after 6 h half is full, A fills the other half in 2 h: III true.

13.  
2 men or 3 women can finish a job in 24 days. In how many days will 4 men and 3 women finish it together?

Correct Answer: B [8 days]

Explanation:

1 woman = 2/3 man → 4 men + 3 women = 6 men; 48 man-days ÷ 6 = 8 days.

14.  
Reverse question: A and B together finish a job in 6 days, and A alone takes 5 days less than B alone. How many days does A alone take?

Correct Answer: C [10]

Explanation:

Try options: A = 10, B = 15 → 10 × 15/25 = 6 days.

15.  
Three pipes A, B and C can fill a tank in 10, 12 and 15 hours respectively. If all three are opened together, the tank fills in:

Correct Answer: D [4 hours]

Explanation:

LCM 60: 6 + 5 + 4 = 15 units/h → 4 hours.

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