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Work & Wages Questions and Answers

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31.

X can do a work in 15 days and Y in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

Answer: D

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

\[ 4\left(\frac{1}{15} + \frac{1}{20}\right) = 4 \times \frac{4 + 3}{60} = \frac{28}{60} = \frac{7}{15} \]

\[ \text{left} = 1 - \frac{7}{15} = \frac{8}{15} \]

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32.

A, B, and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

Answer: B

LCM of 20, 30, 60 is 60. Total work = 60 units. A's rate=3, B's rate=2, C's rate=1 unit/day. A works alone for the first two days, doing \(3+3=6\) units. On the third day, A, B, and C work together, doing \(3+2+1=6\) units. So, in a 3-day cycle, \(6+6=12\) units of work are done. To complete 60 units, we need \(60/12 = 5\) such cycles. The total time taken is \(5 \times 3 = 15\) days.

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33.

A is twice as efficient as B and B is thrice as efficient as C. If they together can complete the work in 10 days, in how many days can A alone do it?

Answer: B

Let C's efficiency be x. Then B's is 3x and A's is 2*(3x)=6x. Their combined efficiency is x+3x+6x = 10x. Total work = \(10x \times 10 = 100x\). Time taken by A alone = Total work / A's efficiency = \(100x / 6x = 100/6 = 50/3 = 16.67\) days.

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34.

A and B can do a job together in 7 days. A is 1 3/4 times as efficient as B. The same job can be done by A alone in:

Answer: B

A is 7/4 times as efficient as B. The ratio of their efficiencies A:B is 7:4. Combined efficiency = 11 units (say). Total work = \(11 \times 7 = 77\) units. Time for A alone = Total work / A's efficiency = 77 / 7 = 11 days.

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35.

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

Answer: C

Let W be woman's work, C be child's work. From the problem, \(10W \times 7 = 10C \times 14 \Rightarrow 70W = 140C \Rightarrow W=2C\). Total work = \(10W \times 7 = 10(2C) \times 7 = 140C\). We need time for 5 women and 10 children. Their combined rate = \(5W+10C = 5(2C)+10C = 10C+10C=20C\). Time = Total work / Rate = 140C / 20C = 7 days.

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36.

A pipe can fill a tank in 15 minutes and another can empty it in 20 minutes. If the tank is empty and both pipes are opened together, the tank will be full in:

Answer: C

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

\[ \frac{1}{15} - \frac{1}{20} = \frac{4 - 3}{60} = \frac{1}{60} \]

\[ t = 60 \text{ minutes} \]

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37.

A can build a wall in 30 days, while B alone can build it in 40 days. If they build it together and get a payment of Rs. 7000, what is B's share?

Answer: B

The ratio of their efficiencies is inversely proportional to the time they take. Ratio of time A:B = 30:40 = 3:4. Ratio of efficiency A:B = 4:3. The wages will be shared in the ratio of efficiency. B's share = \(\frac{3}{4+3} \times 7000 = \frac{3}{7} \times 7000 = 3000\). B's share is Rs. 3000.

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38.

A garrison of 500 men had provisions for 27 days. After 3 days, a reinforcement of 300 men arrived. For how many more days will the remaining food last now?

Answer: A

The remaining food was supposed to last for 500 men for 27-3 = 24 days. Total remaining food = \(500 \times 24\) man-days. Now, the number of men is \(500+300=800\). The food will last for \((500 \times 24) / 800 = 12000 / 800 = 15\) days.

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39.

A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it alone?

Answer: A

Let B do W work in T time. Then A does W/2 work in 3T/4 time. B's rate = W/T. A's rate = (W/2)/(3T/4) = 2W/3T. The ratio of their rates A:B = (2W/3T) : (W/T) = 2/3 : 1 = 2:3. Combined rate is 5 units. Total work = \(5 \times 18 = 90\) units. B's rate is 3 units/day. Time for B alone = 90/3 = 30 days.

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40.

Two pipes can fill a tank in 10 and 12 hours respectively while a third pipe can empty the full tank in 20 hours. If all three pipes operate simultaneously, in how much time will the tank be filled?

Answer: B

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

\[ \frac{1}{10} + \frac{1}{12} - \frac{1}{20} = \frac{6 + 5 - 3}{60} = \frac{8}{60} = \frac{2}{15} \]

\[ t = \frac{15}{2} = 7.5 \text{ h} = 7 \text{ hr } 30 \text{ min} \]

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