Question

If $12$ men and $16$ boys can do piece of work in $5$ days and if $13$ men and $24$ boys can do it in $4$ days, how long will $7$ men and $10$ boys take to do it ?

• A. $3\frac{2}{3}$ Days
• B. $8\frac{1}{3}$ Days
• C. $4\frac{5}{3}$ Days
• D. $9\frac{1}{3}$ Days

Answer 1

The correct option is B $8\frac{1}{3}$ Days

Let 1 man's 1 day's work=x

and 1 boy's 1 day's work=y

Then according to the question

$12x+16y=\frac{1}{5}$ and $13x+24y=\frac{1}{4}$

$\Rightarrow 60x+80y=1$..................................................................(1)

$\Rightarrow 52x+96y=1$..................................................................(2)

Multiply the (1 ) by 6 and (2) by 5

$⟹360x+480y=6$.............................................................(3)

$⟹260x+480y=5$............................................................(4)

Add the both equation

$\Rightarrow 100x=1$

$\Rightarrow x=\frac{1}{100}$

put the value of x in (1) we get

$⟹60\times \frac{1}{100}+80y=1$

$⟹80y=1-\frac{6}{10}$

$⟹80y=\frac{10-6}{10}$

$⟹80y=\frac{4}{10}$

$⟹y=\frac{1}{200}$

$\therefore$ (7 men+ 10 boy's 1 day's work=$(\frac{7}{100}+\frac{10}{200})=\frac{12}{100}$

$\therefore$7 Men 10 boy's do the work in $\frac{100}{12}=8\frac{1}{3}days$