Question

What 2 mansons earn in a day is earned by 3 male workers in a day. The daily wages of 15 female workers is €30 more than the total daily wages of 5 masons and 3 male workers. If one mason, one male worker and 2 female workers are engaged for a day, the builder has to pay €160 as wages. Find the daily wages of a mason, a male worker and a female worker.

Answer 1

Given

The pay of different types of workers

To find

Daily wages of a mason, a male worker and a female worker

Solution

Let

x be the daily wage of mason

y be the daily wage of male workers

z be the daily wage of female workers

$2x=3y\\\Rightarrow y=\dfrac{2}{3}x\quad ...(i)$

$15z=30+5x+3y\\\Rightarrow -5x-3y+15z=30\quad ...(ii)$

$x+y+2z=160\quad ...(iii)$

Applying (i) to (ii)

$-5x-3\dfrac{2}{3}x+15z=30\\\Rightarrow -7x+15z=30\quad ...(iv)$

Applying (i) to (iii)

$x+\dfrac{2}{3}x+2z=160\\\Rightarrow 5x+6z=480\quad ...(v)$

(iv)-(v)

$-7x+15z=30$

$5x+6z=480$$\times\dfrac{5}{2}$

$-7x+15z=30$

$\dfrac{25}{2}x+15z=1200\quad ...(vi)$

(iv)-(vi)

$-\dfrac{39}{2}x=-1170\\\Rightarrow x=1170\times\dfrac{2}{39}\\\Rightarrow x=60$

$y=\dfrac{2}{3}x=\dfrac{2}{3}\times 60\\\Rightarrow y=40$

$x+y+2z=160\\\Rightarrow z=\dfrac{160-x-y}{2}=\dfrac{160-60-40}{2}\\\Rightarrow z=30$

So, the mason earns €60, the male worker earns €40 and the female worker earns €30 daily.