Question

4 men and 6 woman get Rs 1600 by doing a piece of work in 5 days. 3 men and 7 woman get Rs 1740 by doing the same work in 6 days. In how many days, 7 men and 6 woman can complete the same work getting Rs 3760?

• A. $6$ days
• B. $8$ days
• C. $10$ days
• D. $12$ days

Answer 1

The correct option is B $8$ days

In $5$ days ,($4$ men$+6$ women) get $=$Rs $1600$

$\therefore$, In $1$ day, ($4$ men$+6$ women) get $=\frac{1600}{5}=$Rs.$320$ ...$\left(1\right)$

In $1$ day, number of persons to get Re.$1=\frac{320}{4men+6women}$ ....$\left(2\right)$

Similarly, in second condition,

In $1$ day, number of person to get Re.$1$

$=\frac{1740}{6\times (3men+7women)}=\frac{290}{3men+7women}$ ...$\left(3\right)$

From Eqs.$\left(2\right)$ and $\left(3\right)$ We get

$\frac{320}{3men+7women}=\frac{290}{3men+7women}$

$96$ men$+224$women$=116$ men$+174$women

$\Rightarrow 20men=50women$

$\Rightarrow \frac{man}{woman}=\frac{5}{2}$

$\therefore ,1$ woman$=\frac{2}{5}$ man

from Eq.$\left(2\right)$ in $1$ day,

$(4men+6women)=(4men+6\times \frac{2}{5}m)$ $=\frac{32}{5}mengetRs.320$

In $1$ day , $1$ man get$\frac{320\times 5}{32}=Rs.50$

$\therefore$ In $1$ day, $1$ woman get $\frac{50\times 2}{5}=Rs.20$

$\therefore$, in $1$ day $(7men+6women)get7\times 50+6\times 20=Rs.470$

Let, required number of days $=\frac{3760}{470}=8$days