Question

If the wage of $45$ women amounts to $₹15525$ in $48$ days, how many men must work for $16$ days to receive $₹5750$, the daily wage of a man being double that of a woman?

Answer 1

Calculate the number of men to receive the amount.

As we know that, If ${\mathrm{M}}_1$ person can do ${\mathrm{W}}_1$ works in ${\mathrm{D}}_1$ days and ${\mathrm{M}}_2$ work in ${\mathrm{D}}_2$ days, then we have,

${\mathbf{M}}_{\mathbf{1}}\mathbf{\times }{\mathbf{D}}_{\mathbf{1}}\mathbf{\times }{\mathbf{W}}_{\mathbf{2}}\mathbf{=}{\mathbf{M}}_{\mathbf{2}}\mathbf{\times }{\mathbf{D}}_{\mathbf{2}}\mathbf{\times }{\mathbf{W}}_{\mathbf{1}}$

It is given that, the wage of $45$ women amounts to $₹15525$ in $48$ days.

It is required to find the number of men to receive $₹5750$.

We will find the number of required men by using the Time and Work formula is,

${\mathbf{M}}_{\mathbf{1}}\mathbf{\times }{\mathbf{D}}_{\mathbf{1}}\mathbf{\times }{\mathbf{E}}_{\mathbf{1}}\mathbf{\times }{\mathbf{W}}_{\mathbf{2}}\mathbf{=}{\mathbf{M}}_{\mathbf{2}}\mathbf{\times }{\mathbf{D}}_{\mathbf{2}}\mathbf{\times }{\mathbf{E}}_{\mathbf{2}}\mathbf{\times }{\mathbf{W}}_{\mathbf{1}}$

Where, $\mathrm{E}$ is efficiency or wages and $\mathrm{W}$ is the work or amount.

According to the question,

${\mathrm{M}}_1=45$

${\mathrm{D}}_1=48$

${\mathrm{E}}_1=1$

${\mathrm{W}}_1=15525$

${\mathrm{D}}_2=16$

${\mathrm{E}}_2=2$

${\mathrm{W}}_2=5750$

${\mathrm{M}}_2=?$

Put all the values in the formula for Time and Work.

$\Rightarrow$ $45\times 48\times 1\times 5750={\mathrm{M}}_2\times 16\times 2\times 15525$

$\Rightarrow$ $12420000={\mathrm{M}}_2\times 496800$

$\Rightarrow$ ${\mathrm{M}}_2=\frac{12420000}{496800}$

$\Rightarrow$ ${\mathrm{M}}_2=25$

Therefore, $25$ men are required to work for $16$ days to receive $₹5750$.