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Work & Wages Questions and Answers

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51.

A, B, and C can do a job in 6, 12 and 15 days respectively. After 1/8 of the work is completed, C leaves the job. Rest of the work is done by A and B together. Time taken to complete the rest of the work is:

Answer: A

Work in rates: someone who finishes a job in \( n \) days does \( \tfrac{1}{n} \) of it a day, and rates add.

Once \( \tfrac{1}{8} \) is done, \( \tfrac{7}{8} \) remains for A and B:

\[ \frac{1}{6} + \frac{1}{12} = \frac{2 + 1}{12} = \frac{1}{4} \]

\[ t = \frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times 4 = 3.5 = 3\tfrac{1}{2} \text{ days} \]

C's rate never enters the calculation, since C leaves before the stretch being timed.

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52.

A work could be completed in 100 days by some workers. However, due to the absence of 10 workers, it was completed in 110 days. The original number of workers was:

Answer: B

Let the original number of workers be x. Using the man-days formula M1*D1 = M2*D2. \(x \times 100 = (x-10) \times 110 \Rightarrow 100x = 110x - 1100 \Rightarrow 10x = 1100 \Rightarrow x = 110\). The original number of workers was 110.

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53.

A and B can do a work in 10 days. They start the work together but A leaves after 2 days and B completes the rest of the work in 12 days. In how many days can A do the work alone?

Answer: D

Work done by A and B in 2 days = 2/10 = 1/5. Remaining work = 4/5. B completes 4/5 of the work in 12 days. So B can complete the full work in \(12 \times 5/4 = 15\) days. B's one day work is 1/15. (A+B)'s one day work is 1/10. A's one day work = \(1/10 - 1/15 = (3-2)/30 = 1/30\). A alone takes 30 days.

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54.

A can do 1/3 of a work in 5 days and B can do 2/5 of the work in 10 days. In how many days both A and B together can do the work?

Answer: C

A can do the full work in \(5 \times 3 = 15\) days. B can do the full work in \(10 \times 5/2 = 25\) days. A's 1 day work = 1/15. B's 1 day work = 1/25. Together, their 1 day work = \(1/15 + 1/25 = (5+3)/75 = 8/75\). They will take 75/8 = 9 3/8 days.

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55.

A is 50% as efficient as B. C does half of the work done by A and B together. If C alone does the work in 20 days, then A, B and C together can do the work in:

Answer: B

Let B's efficiency be 2 units/day. Then A's is 1 unit/day. A+B together do 3 units/day. C does half of this, so C's efficiency is 1.5 units/day. C takes 20 days, so total work = \(1.5 \times 20 = 30\) units. All three together have an efficiency of 1+2+1.5 = 4.5 units/day. Time taken together = 30 / 4.5 = 300 / 45 = 20/3 = 6 2/3 days.

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56.

If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work?

Answer: A

From the problem, 3 men = 6 women, so 1 man = 2 women. We need to find the time for 12 men and 8 women. Convert men to women: 12 men = 24 women. Total equivalent women = 24+8=32 women. We know 6 women take 16 days. Using M1D1=M2D2, \(6 \times 16 = 32 \times D2 \Rightarrow 96 = 32 \times D2 \Rightarrow D2 = 3\) days.

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57.

Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full?

Answer: B

LCM of 6 and 4 is 12. Total work = 12 units. A's rate=2, B's rate=3 units/hour. In the first hour, A fills 2 units. In the second hour, B fills 3 units. In a 2-hour cycle, 5 units are filled. After 2 cycles (4 hours), 10 units are filled. Remaining work is 2 units. It is A's turn. A will fill the remaining 2 units in 1 hour. Total time = 4 + 1 = 5 hours.

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58.

A can write 75 pages in 25 hours. A and B together can write 135 pages in 27 hours. In what time can B write 42 pages?

Answer: C

A's writing rate = 75 pages / 25 hours = 3 pages/hour. (A+B)'s writing rate = 135 pages / 27 hours = 5 pages/hour. B's writing rate = (A+B)'s rate - A's rate = 5 - 3 = 2 pages/hour. Time for B to write 42 pages = Total pages / B's rate = 42 / 2 = 21 hours.

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59.

A and B can do a work in 18 and 24 days respectively. They worked together for 8 days and then A left. The remaining work was finished by B in:

Answer: A

LCM of 18 and 24 is 72. Total work = 72 units. A's rate=4, B's rate=3 units/day. Work done in 8 days together = \((4+3) \times 8 = 56\) units. Remaining work = 72 - 56 = 16 units. Time for B to finish this = 16 / 3 = 5 1/3 days.

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60.

A, B and C get Rs. 575 for a work. A and C are supposed to finish 19/23 of the work together. How much amount shall be paid to B?

Answer: A

Pay follows the share of work done.

\[ \text{B's share} = 1 - \frac{19}{23} = \frac{4}{23} \]

\[ 575 \times \frac{4}{23} = \text{Rs. } 100 \]

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