3 women and 1 girl together can complete a work in 25 days. 2 women and 5 girls can together complete half of the same work in 9 days. Find the time taken by 1 woman and 1 girl together to complete 40% of the entire work.

Solution

Let the efficiency of woman and that of a girl be 'X' units/day and 'Y' units/day respectively. Time taken by 2 women and 5 girls together to complete the entire work = 9 × 2 = 18 days Then, total work = (3X + Y) × 25 = (2X + 5Y) × 18 Or, 75X + 25Y = 36X + 90Y Or, 39X = 65Y So, X:Y = 65:39 = 5:3 Let 'X' = '5a' and 'Y' = '3a' Then, total work = (5a × 3 + 3a) × 25 = '450a' units 40% of the total work = 450a × 0.4 = '180a' units Time taken by 1 woman and 1 girl together to complete 40% of the work = 180a ÷ (5a + 3a) = (180a/8a) = 22.5 days