Question

A certain number of men are twice as many women and thrice as many boys, earn Rs. $5100$ in $6$ days. A woman earns one and a half times as a boy and a man as much as a woman and a boy earn together per day. How many women were there if a boy earned Rs. $25$ daily ?

• A. $4$
• B. $7$
• C. $12$
• D. $36$

Answer 1

The correct option is B $7$

Let the no. of men, women, and boys be $x,y,$ and $z$ respectively.

$\therefore$ According to the question:

$x=2y$ ...... $\left(i\right)$

$x=3z$ ...... $\left(ii\right)$

Let the money earn by a man, a woman, and a boy be Rs. $a,$ Rs. $b$ and Rs. $c$ per day respectively

$x$ men earn Rs $5100$ in $6$ days

$\therefore$ Money earned by $x$ men in $1$ day $=\frac{5100}{6}=850$

$\Rightarrow$ Money earned by $1$ men in $1$ day $=\frac{850}{x}=a$ ..... $\left(iii\right)$

Now according to the question:

A woman earns one and a half times as a boy earn and a man as much as a woman and a boy together earn per day.

$b=\frac{3}{2}c$ ...... $\left(iv\right)$

$a=b+c$ ...... $\left(v\right)$

From equation $\left(iv\right)$ and $\left(v\right)$, we have

$a=\frac{3}{2}c+c=\frac{5}{2}c$

Given that a boy earns Rs. $25$ daily

$\therefore c=25$

$a=\frac{5}{2}\times 25=\frac{125}{2}$

From equation $\left(iii\right)$, we have

$\frac{850}{x}=\frac{125}{2}$

$\Rightarrow x=850\times \frac{2}{125}=\frac{68}{5}$

Now from equation $\left(i\right)$, we have

$\frac{68}{5}=2\times y$

$\Rightarrow y=6.8$

No. of women $=6.8\approx 7$