A 100 m long 3 m high and 30 cm wide wall is built by 30 men, 20 women and 50 children working 9 hours a day in 20 days. How long a wall 1.5 m high 30 cm wide can be built by 15 men, 25 women and 35 children working 2 hour a day in 15 days (given men, women and children are equally efficient)?

Question: A 100 m long 3 m high and 30 cm wide wall is built by 30 men, 20 women and 50 children working 9 hours a day in 20 days. How long a wall 1.5 m high 30 cm wide can be built by 15 men, 25 women and 35 children working 2 hour a day in 15 days (given men, women and children are equally efficient)?Solution:Earlier dimensions of the wall = 100 × 3 × 0.30.Volume of the wall = 90New dimensions = L × 1.5 × 0.3.Volume of the wall = 0.45L∴ As men, women and children are given to be equally efficient, so in the first case, the total number of persons is (30 + 20 + 50) = 100 and the same in the second case is (15 + 25 + 35) = 75working 9 hours a day in 20 days 100 persons make 90 m3 wall∴ working 1 hours a day in 1 days 1 persons make 90/(100 × 20 × 9) m3 wall∴ working 2 hours a day in 15 days 75 persons make (90 × 75 × 15 × 2)/(100 × 20 × 9) m3 wall= 11.25∴ Length of the wall = L = 11.25/0.45 = 25 m