Shortcut Trick
Efficiency Ratio (W:M) ⇒ 10W × 16 : 6M × 8 ⇒ 160 : 48 ⇒ 10 : 3 (W=3, M=10).
Total Work = 10 × 3 × 16 = 480 units.
Work done by 12 men in 2 days = 12 × 10 × 2 = 240 units.
Remaining Work = 480 − 240 = 240 units.
New Efficiency (6M + 5W) = (6 × 10) + (5 × 3) = 75 units/day.
Total time = 2 + (240 ÷ 75) = 2 + 16/5 = 26/5 days.
∴ The correct answer is 26/5 days.
Alternate Method
Given:
Work completed by 10 women in 16 days.
Work completed by 6 men in 8 days.
Initial workforce: 12 men for 2 days.
New workforce: 6 men (12 − 6) and 5 women.
Formula Used:
Total Work = Number of persons × Efficiency × Time
Calculations:
⇒ 10 Women × 16 days = 6 Men × 8 days
⇒ 160W = 48M ⇒ 10W = 3M ⇒ M/W = 10/3
⇒ Efficiency of 1 Man (M) = 10 units, 1 Woman (W) = 3 units
⇒ Total Work = 48 × 10 = 480 units
⇒ Work done in first 2 days = 12M × 2 = 12 × 10 × 2 = 240 units
⇒ Remaining Work = 480 − 240 = 240 units
⇒ Efficiency of new group (6M + 5W) = 6(10) + 5(3) = 60 + 15 = 75 units/day
⇒ Time for remaining work = 240 ÷ 75 = 16/5 days
⇒ Total time taken = 2 + 16/5 = 26/5 days
∴ The correct answer is 26/5 days.
Additional Information
Work-Efficiency Relationship
Total work is the product of number of workers, their efficiency, and the time taken (Work = M × E × D). For the same work, (M1D1E1) = (M2D2E2).
Combined Efficiency
When different types of workers (men, women, children) work together, their net efficiency is the sum of their individual efficiencies multiplied by their respective counts.
Fractional Days
If work is not finished in a whole number of days, the time is expressed as (Total Work Done) / (Work done per day), often leading to improper fractions like 26/5.