Shortcut Trick Equate total work: (19M + 13W) × 12 = (17M + 9W) × 14 ⇒ 6(19M + 13W) = 7(17M + 9W) ⇒ 114M + 78W = 119M + 63W ⇒ 119M − 114M = 78W − 63W ⇒ 5M = 15W ⇒ 1M = 3W ∴ The correct answer is 3 women. Alternate Method Given: 19 Men (M) and 13 Women (W) take 12 days. 17 Men and 9 Women take 14 days. Formula Used: Total Work = (Efficiency × Time) +---------+-------------+-----------------------+ | Group | Time (Days) | Total Work Expression | +---------+-------------+-----------------------+ | Group 1 | 12 | 12 × (19M + 13W) | | Group 2 | 14 | 14 × (17M + 9W) | +---------+-------------+-----------------------+ Calculations: ⇒ 12 × (19M + 13W) = 14 × (17M + 9W) ⇒ 228M + 156W = 238M + 126W ⇒ 238M − 228M = 156W − 126W ⇒ 10M = 30W ⇒ 1M = 3W ∴ The correct answer is 3 women. Related Concepts: Work Equality Principle When different groups complete the same work, we use M_(1)D_(1) = M_(2)D_(2) to find the ratio of efficiencies. Man-Days Concept Total work is often expressed in terms of Man-days or Woman-days, which is the product of the number of people and the time taken. Efficiency Ratio If 1 man is equivalent to 'n' women, the efficiency ratio M:W is n:1.