### Question 4

SSC-CGL 2020 Mar 4 Shift 3

4 men and 6 women can do a work in 5 days. 3 men and 4 women can do the same work in 7 days. How many men will assist 25 women to complete 2-1/2 times the same work in 5 days?

### Solution in Detail

Let the efficiency of 1 man = M

and of 1 woman = W

Efficiency [def.] is the work done in 1 unit of time, which is 1 day in this question.Total work by first condition

$\displaystyle (4M + 6W) \times 5\text{. . . (1)}$

Total work by second condition

$\displaystyle (3M + 4W) \times 7\text{. . . (2)}$

Equating and simplifying,

$\displaystyle M = 2W$

given 4 men + 6 women can finish the work in 5 days

$\displaystyle \therefore (4M + 6W) \equiv 14W$

Work to be done $\displaystyle 2\frac12$ times, so woman required are

$\displaystyle = 14W \times \frac52 = 35W$

We already have $\displaystyle 25W$

Additional requirement $\displaystyle = 10W$

$\displaystyle \equiv 5M \text{ i.e., } 5 \text{ men }\underline{Ans}$

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