If 16 women and 24 men can complete a work in 18 days, how many days will 24 men take to complete the same work, given that each woman takes twice as long as a man to complete the work?

Hey kesharoli2024, good to see you again. Step 1: Determine the relationship between the work rates of a man and a woman. The problem states that each woman takes twice as long as a man to complete the work. This means a man works twice as fast as a woman. Let M be the work rate of one man (work per day) and W be the work rate of one woman (work per day). Therefore, the work rate of a woman is half the work rate of a man: W = (1)/(2) M Step 2: Calculate the combined work rate of 16 women and 24 men in terms of men's work rate. The combined work rate is 16W + 24M. Substitute W = (1)/(2) M: 16((1)/(2) M) + 24M = 8M + 24M = 32M So, 16 women and 24 men together have a work rate equivalent to 32 men. Step 3: Calculate the total amount of work. The group of 16 women and 24 men (equivalent to 32 men) completes the work in 18 days. Total Work = (Equivalent men's work rate) × (Time taken) Total Work = 32M × 18 days Step 4: Calculate the number of days 24 men will take to complete the same work. Let D be the number of days 24 men will take. The work rate of 24 men is 24M. Total Work = 24M × D Equate the total work from Step 3 and this expression: 32M × 18 = 24M × D Divide both sides by M (assuming M ≠ 0): 32 × 18 = 24 × D Solve for D: D = (32 × 18)/(24) D = (576)/(24) D = 24 Thus, 24 men will take 24 days to complete the work. The number of days 24 men will take to complete the work is 24 days. Send me the next one 📸