Question : 1 man and 4 women can complete a work in $\frac{65}{4}$ days, while 3 men and 4 women can complete it in $\frac{13}{2}$ days. In how many days will 13 women complete the same?
Option 1: 20
Option 2: 16
Option 3: 14
Option 4: 18
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Correct Answer: 20
Solution :
As they are doing the same work
⇒ $M{_1}D{_1} =M{_2}D{_2}$, where $M_1$ and $M_2$ = the number of men and $D_1$ and $D_2$ = the number of days
⇒ $(M + 4W) × \frac{65}{4} = (3M + 4W) × \frac{13}{2}$
⇒ $(M + 4W) × \frac{5}{2} = (3M + 4W)$
⇒ $5M + 20W = 6M + 8W$
$\therefore M = 12W$
Let the efficiency of M = 12
and the efficiency of W = 1
⇒ Total Efficiency of 1 man and 4 women $= (12 + 4 × 1) = 12 + 4 = 16$
⇒ Total work = Efficiency × Time = $16 × \frac{65}{4}$ = 260
⇒ Efficiency of 13 women $= 13 × 1 = 13$
$\therefore$ Time taken by 13 women to do the work $= \frac{260}{13} = 20$ days
Hence, the correct answer is 20.
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