Question 13 A work can be completed in 12 days if 2 men and 3 women work together.
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A work can be completed in 12 days if 2 men and 3 women work together. It can be completed in 8 days if 4 men and 4 women are involved.
How long it will take to complete the work by 16 women and 8 men?
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Show answer & explanation
Equating total work gives 12(2m + 3w) = 8(4m + 4w), yielding w = 2m. Total work is 96m. 16 women and 8 men have an effective rate of 40m per day, taking 96/40 = 12/5 days.
Step-by-step Derivation:
Step 1: Total work W = 12 * (2m + 3w) = 24m + 36w.
Step 2: Also W = 8 * (4m + 4w) = 32m + 32w.
Step 3: Equating: 24m + 36w = 32m + 32w => 4w = 8m => 1w = 2m.
Step 4: Total work W = 24m + 36(2m) = 96m.
Step 5: Group of 16 women + 8 men = 16(2m) + 8m = 40m.
Step 6: Time required = 96m / 40m = 12/5 days.