Question : A man alone can paint a house in 9 days and a woman alone can paint the house in 18 days. If 3 men and 3 women worked together, then in how many days they will paint the house?
Option 1: 4 days
Option 2: 3 days
Option 3: 2 days
Option 4: 6 days
Correct Answer: 2 days
Solution :
Time taken by a man to complete the work = 9 days
$\therefore$ Part of the work done by 1 man in a day = $\frac{1}{9}$
Time taken by a woman to complete the work = 18 days
$\therefore$ Part of the work done by 1 woman in a day = $\frac{1}{18}$
⇒ Part of the work done by 3 men and 3 women in a day
= $\frac{3}{9}$+ $\frac{3}{18}$
= $\frac{1}{3}$+ $\frac{1}{6}$
= $\frac{2+1}{6}$
= $\frac{1}{2}$
So, the time taken by 3 men and 3 women to complete the work = 2 days
Hence, the correct answer is 2 days.
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