Question : 2 men can finish a work in 6 days and 3 women can finish the same work in 4 days. How many days will 1 man and 2 women finish the work if they work together daily?
Option 1: 4
Option 2: 6
Option 3: 8
Option 4: 9
Correct Answer: 4
Solution :
Let Male = $m$; Female = $w$
Work = Rate $\times$ Time
2 men can finish the work in 6 days (assuming total work as 1 unit)
$\therefore 2m\times 6 = 1$
⇒ $m = \frac{1}{12}$
And 3 women can finish the same work in 4 days.
$\therefore$ $3w\times 4 = 1$
⇒ $w = \frac{1}{12}$
Now, we need to find the rate at which 1 man and 2 women work together. The combined rate is $(1m+2w)$.
$(1m + 2w)$ × Time = 1
⇒ $(\frac{1}{12}+\frac{2}{12})$ × Time = 1
⇒ $(\frac{3}{12})$ × Time = 1
$\therefore$ Time = 4 days
Hence, the correct answer is 4.
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