Correct option is D
Given:
5 men and 2 women can reap 48 hectares in 3 days.
3 men and 1 woman can reap 54 hectares in 6 days.
Work to be done: 6 men and x women reap 378 hectares in 14 days.
Formula Used:
Work = Rate × Time
Solution:
Let the daily work done by 1 man be M and 1 woman be W.
For the first group:
(5M + 2W) × 3 = 48
5M + 2W = 16 ... (Equation 1)
For the second group:
(3M + 1W) × 6 = 54
3M + W = 9 W = 9 - 3M ... (Equation 2)
Substitute Equation 2 into Equation 1:
5M + 2(9 - 3M) = 16
5M + 18 - 6M = 16
-M = -2 M = 2
Substitute M back to find W:
W = 9 - 3(2) = 9 - 6 = 3
Now, for the final task, let x be the number of women required:
(6M + xW) × 14 = 378
6M + xW = \frac{378}{14} = 27
Substitute M = 2 and W = 3:
6(2) + x(3) = 27
12 + 3x = 27
3x = 15
x = 5
Final Answer
So the correct answer is (d)
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