Question

The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and by a boy in 12 hours.If working 6 hours per day 9 men can complete a work in 6 days then in how many days can 12 men 12 women and 12 boys together finish the same work working 8 hours per day ?

• A. 3\(\frac{2}{3}\)
• B. 4\(\frac{1}{2}\)
• C. 3days
• D. 1\(\frac{1}{2}\)

Answer 1

The Correct Option is D

Let take the value of men be M and value of boy be B and value of women be W.
6M=8W=12B
3m =4w =6b – Equation 1
X = 12m+12w+12b – Equation 2
After Equating both the equation, we get
1m = 2b
1w = \(\frac{6}{4b}\)
After putting it in equation 2, we get
 X= 24b + 18b + 12b
X = 54b
So, 9m × 6 × 6 = X × 8 × D (Here D is number of days)
54 × 6 × 2b =54b × 8 × D
D = \(\frac{3}{2}\)
D = 1.5 days
The correct option is (D)