Question

4 men and 6 boys can finish a piece work in 5 days while 3 men and 4 boys can finish it in 7 days. find the time taken by 1 man alone or that by 1 boy alone.

Answer 1

Answer:

Number of days taken by 1 man alone and 1 boy alone are 35 days and 70 days respectively.

Step-by-step explanation:

Let, the work completed by 1 man in 1 day = x and the work completed by 1 boy in 1 day = y.

So, 4 men and 6 boy's 1 day work is $\frac{4}{x}$ and $\frac{6}{y}$

And, 3 men and 4 boy's 1 day work is $\frac{3}{x}$ and $\frac{4}{y}$

Since, 4 men and 6 boys complete the work in 5 days and 3 men and 4 boys complete the work in 7 days.

So, we have,

$\frac{4}{x}+\frac{6}{y}=\frac{1}{5}$

$\frac{3}{x}+\frac{4}{y}=\frac{1}{7}$

Let, $u=\frac{1}{x}$ and $v=\frac{1}{y}$

So, the equations are,

$4u+6v=\frac{1}{5}$  ................(1)

$3u+4v=\frac{1}{7}$  ................(2)

Multiply (1) by 3 and (2) by 4 and subtract the equations, we get,

$2v=\frac{1}{35}$ i.e. $v=\frac{1}{70}$ i.e. $\frac{1}{y}=\frac{1}{70}$ i.e. y = 70.

Substitute value of 'v' in (1) gives,

$4u+\frac{6}{70}=\frac{1}{5}$ i.e. $4u=\frac{-6}{70}+\frac{1}{5}$ i.e. $4u=\frac{8}{70}$ i.e. $u=\frac{8}{70\times 4}$ i.e. $u=\frac{1}{35}$ i.e. $\frac{1}{x}=\frac{1}{35}$ i.e. x = 35

So, the number of days taken by 1 men alone and 1 boy alone are 35 days and 70 days respectively.