Question

If 14 men and 12 boys can finish work in 4 days, while 8 men and 16 boys can finish the same work in 5 days. Compare the 1 day work of 1 man and 1 boy.

Answer 1

hope this will hlp u

Answer 2

1 man complete the work in 80 days and the boys can complete the work in 160 days

Solution:

Let the work completed by men in x days

The work done by a men in 1 day = $\frac{1}{x}$

Let the work completed by boys in y days

The work done by a men in 1 day = $\frac{1}{y}$

As per question we can frame equation as follows:-

$\begin{array}{l}{14 \times\left(\frac{1}{x}\right)+12 \times\left(\frac{1}{y}\right)=4} \\\\ {\text {Also } 8 \times\left(\frac{1}{x}\right)+16 \times\left(\frac{1}{y}\right)=5}\end{array}$

$\text {Now on replacing, } \frac{1}{x}=a \text { and } \frac{1}{y}=b \text { we get }$

$14 a+12 b=\frac{1}{4}$  ------- eqn 1

$8 a+16 b=\frac{1}{5}$  ------- eqn 2

On solving above two equations we get

By multiplying Equation (1) with 4 and Equation (2) with 3 we get ,

$56 a+48 b=\frac{1}{4} \times 4$

56a + 48b = 1   ------- eqn 3

$24 a+48 b=\frac{1}{5} \times 3$

$24 a+48 b=\frac{3}{5}$  ----- eqn 4

On subtracting Equation (4) from Equation(3) we get,

$\begin{array}{l}{32 a=1-\frac{3}{5}=\frac{2}{5}} \\\\ {\Rightarrow a=\frac{2}{32 \times 5}=\frac{1}{80}}\end{array}$

$\text {And we get } \mathrm{b}=\frac{1}{160}$

$\text {since, } x=\frac{1}{a}=80 \text { and } y=\frac{1}{b}=160$

So, 1 man complete the work in 80 days and the boys can complete the work in 160 days

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