2 men and 1 woman can do a piece of work in 14 days. while 4 women and 2 men can do the same work in 8 days. If a man gets Rs.90 per day, what should be the wages per day of a women?

A) Rs.48

B) Rs.60

C) Rs.72

D) Rs.135

Correct answer:
B) Rs.60

Description for Correct answer:

Let man be represent by m and woman be represented by w.

Because, 2m + 1w = \( \Large \frac{1}{14} \)

= \( \Large 14 \times \left(2m+1w\right)=1 \) ...(i)

and \( \Large 4w + 2m = \frac{1}{8} \)

\( \Large 8 \left(4w+2m\right)=1 \) ...(ii)

On equating Eqs. (i) and (ii), we get

\( \Large 14 \times \left(2m+1w\right)=8 \times \left(4w+2m\right) \)

\( \Large 28m + 14w = 32w + 16m \)

= 28m + 14w = 32w + 16m

= 28m -16m = 32w -14w

= 12m = 18w

\( \Large \frac{m}{w} = \frac{18}{12} = \frac{3}{2} \)

So, efficiency of 1 man and 1 woman is c : 2

So, their wages must be in the same ratio

\( \Large \frac{90}{x} = \frac{3}{2} \)

[here, x = wages of a woman]

Therefore, x = \( \Large \frac{90 \times 2}{3} \) = Rs.60



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