Question

If $3$ men with $4$ boys can earn $Rs.210$ in $7$ days and $11$ men with $13$ boys can earn $Rs.830$ in $8$ days, in what time will $7$ men with $9$ boys earn $Rs.1100$?

• A. $6days$
• B. $16days$
• C. $10days$
• D. $12days$

Answer 1

Answer: (B)

$16days$

$(3men+4boys)$ can earn $Rs.(210+7)$, i.e., $Rs.30.00$ in one day. And $(11men+13boys)$ can earn $Rs.(830÷8)$, i.e., $Rs.103.75$ in one day. Find out the earning of $1$ man and $1$ boy and then proceed.
$\begin{array}{cc}3m+4b& =30.00\\ 11m+13b& =103.75\end{array}\}\Rightarrow 1m=5,1b=3.75$
Wages for $7m+9b=7\times 5+9\times 3.75=Rs.68.75$ per day
$\therefore$ No. of required days $=Rs.1100+Rs.68.75=16$