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 it take for one man and one boy to do it

Answer 1

Answer:

One man takes 15 days and one boy takes 60 days to do the piece of work

Step-by-step explanation:

Let the amount of work done by 1 man per day be $m$

Let the amount of work done by 1 boy per day be $n$

Given that 2 men and 7 boys can do a piece of work in 4 days

Thus, work done by 2 men and 7 days in 1 day $= \frac{1}{4}$

We get,

$2m + 7n = \frac{1}{4}\\\\8m + 28n = 1$

Similarly,

4 men and 4 boys can do a piece of work in 3 days

Thus, work done by 4 men and 4 days in 1 day $= \frac{1}{3}$

We get,

$4m + 4n = \frac{1}{3}\\\\12m + 12n = 1$

Solving the two equations

 8m + 28n = 1   ---- × 3

 12m + 12n = 1  ---- × 2

-----------------------------------

 24m + 84n = 3

 24m + 24n = 2

(-)        (-)        (-)

---------------------------

           60n = 1

             n = $\frac{1}{60}$

Putting the value of $n$, we get

$12m + 12 \times \frac{1}{60} = 1\\\\ 12m + \frac{1}{5} = 1\\\\12m = 1 - \frac{1}{5}\\\\12m = \frac{4}{5}\\\\m = \frac{4}{(\,5 \times 12)\,}\\\\m = 15$

Thus, Total days taken by 1 man to complete the work $= 15\hspace{0.1cm}days$

Total days taken by 1 boy to complete the work $= 60\hspace{0.1cm}days$