IPMAT Question Paper 2020 | IPM Indore Quants

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Question 20 : Three workers working together need 1 hour to construct a wall. The first worker, working alone, can construct the wall twice as fast at the third worker, and can complete the task an hour sooner than the second worker. Then, the average time in hours taken by the three workers, when working alone, to construct the wall is

1. \\frac{√33 + 4}{3})
2. \\frac{√33 + 5}{3})
3. \\frac{√33 + 6}{3})
4. \\frac{√33 + 7}{3})

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Video Explanation

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Explanatory Answer

Worker	Time taken(in hours)	Work done by each worker in 1 hour
W<sub>1</sub>	n	\\frac{1}{n})
W<sub>2</sub>	n+1	\\frac{1}{n+1})
W<sub>3</sub>	2n	\\frac{1}{2n})

All of them together can complete their work in 1 hour.
\\frac{1}{n}) + \\frac{1}{n+1}) + \\frac{1}{2n}) = 1
\\frac{3}{2n}) + \\frac{1}{n + 1}) = 1
\\frac{3(n + 1) + 2n}{2n(n + 1)}) = 1
3n + 3 + 2n = 2n² + 2n
2n² -3n - 3 = 0
n² - \\frac{3}{2}) n = \\frac{3}{2})
(n - \\frac{3}{4}))² = \\frac{33}{16})
n = \\frac{3}{4}) ± \\frac{√33}{4})
n = \\frac{3 + √33}{4})
Now, we need to find the average which is \\frac{4n + 1}{3})
Substituting n, we get the answer to be \\frac{4 + √33}{3})

The answer is \\frac{√33 + 4}{3})

Choice A is the correct answer.

 

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