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Work & Wages Questions and Answers

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61.

If 1 man or 2 women or 3 boys can do a work in 44 days, then in how many days will 1 man, 1 woman and 1 boy do the work?

Answer: B

From the problem, 1M = 2W = 3B. Let's express everything in terms of boys. 1M = 3B, 1W = 3/2 B. The combined work rate of 1 man, 1 woman, and 1 boy is \(3B + 3/2B + 1B = (6+3+2)/2 B = 11/2 B\). We know 3 boys take 44 days. Using M1D1=M2D2, \(3 \times 44 = (11/2) \times D2 \Rightarrow 132 = 5.5 \times D2 \Rightarrow D2 = 132 / 5.5 = 1320/55 = 24\) days.

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62.

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

Answer: B

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

All three together finish in 3 days, so their combined rate is \( \tfrac{1}{3} \).

\[ \frac{1}{6} + \frac{1}{8} = \frac{4 + 3}{24} = \frac{7}{24} \]

\[ C = \frac{1}{3} - \frac{7}{24} = \frac{8 - 7}{24} = \frac{1}{24} \]

C's share of the work is \( \tfrac{1/24}{1/3} = \tfrac{1}{8} \):

\[ \frac{3200}{8} = \text{Rs. } 400 \]

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63.

Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 32 minutes more to fill the cistern. When the cistern is full, in what time will the leak empty it?

Answer: B

Time taken by two pipes to fill the tank = \(1/14 + 1/16 = (8+7)/112 = 15/112\). So they take 112/15 hours. Due to leakage, time taken = \(112/15 + 32/60 = 112/15 + 8/15 = 120/15 = 8\) hours. Let the leak empty the tank in x hours. So, \(1/14 + 1/16 - 1/x = 1/8 \Rightarrow 15/112 - 1/x = 1/8 \Rightarrow 1/x = 15/112 - 1/8 = (15-14)/112 = 1/112\). So, x = 112 hours.

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Tags: Work and Wages Questions and Answers || Work Efficiency MCQ Questions || Wages Problems GK || Quantitative Aptitude Work MCQ Questions || Work Time and Wages GK