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SSC MTS Model Paper 4

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Question : 28 of 150

Marks: +1, -0

It takes 6 days for 3 women and 2 men working together to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceed that of a woman?

3 times
4 times
5 times
6 times

Solution:

Let the time taken by 3 men = x days

Time taken by 9 women = x + 5 days

3m = x day

2 m =

\frac{3x}{2}

days

Similarly, 9w = x + 5 days

3w = 3(x + 5) days

ATQ,

\frac{2}{3x} + \frac{1}{3(x+5)} = \frac{1}{6}\frac{2x+10+x}{3x(x+5)} = \frac{1}{6}

⇒ 18x + 60 = 3x2 + 15x ⇒ 3x2 − 3x − 60 = 0

Time taken by 1 man = 3x = 3 × 5 = 15 days

Time taken by 1 women = 9(x + 5) = 90 days

Required output = 6 times

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