Question

2 men and 7 boys can do a piece of work in 4 days. It is done by 4 men and 4 boys in 3 days. How long would it take for one man or one boy to do it?

Answer 1

$\mathfrak{\huge{\underline{Solution :}}}$

Let one man can finish the work in x days and one boy can finish the same work in y days.

Then,work done by one man in one day = $\dfrac{1}{x}$

And Work done by one boy in one day = $\dfrac{1}{y}$

$\textbf{\underline{\underline{According\:To\:Question :}}}$

$\implies \sf \: \dfrac{2}{x} + \dfrac{7}{y} = \dfrac{1}{4}..... (eq.i)$

and

$\implies \sf \: \dfrac{4}{ x} + \dfrac{4}{y} = \dfrac{1}{3} .....(eq.ii)$

Let $\dfrac{1}{x}$ be a and $\dfrac{1}{y}$ be b, then :

$\sf \implies \: 2a + 7b = \dfrac{1}{4} .....(eq.iii)$

and

$\sf \implies \: 4a + 4b = \dfrac{1}{3} .....(eq.iv)$

On multiplying (eq.iii) by 2 and subtracting (eq.iv) from it.

$\sf \implies \: 10b = \dfrac{1}{6}$

$\sf \implies \: b = \dfrac{1}{60} \implies \dfrac{1}{y}$

$\sf \therefore\: y = 60 \: days$

Putting b = $\dfrac{1}{60}$ in eq(iii),

$\sf \implies \: 2a + \dfrac{7}{60} = \dfrac{1}{4}$

$\sf \implies \: 2a = \dfrac{1}{4} - \dfrac{7}{60}$

$\sf \implies \: a = \dfrac{1}{15}$

So,

$\sf \: \dfrac{1}{15} = \dfrac{1}{x}$

$\therefore \sf \: x = 15 \: days$

Hence,One man Can finish it in 15 days and boy in 60 days.