Question
4 girls working together for 1
day complete the same amount of work as 6 men working together for 1 day. The efficiency of 1 man is 50% of the efficiency of 1 girl. Additionally, 1 boy, 1 girl, and 1 man together can finish the project in 5 days. How many days will it take for 1 boy to complete the project alone?Solution
ATQ, Since, work done by 4 boy together in 1 day is equal to that done by 6 girls together in 1 day. 4x = 6y 2x = 3y --------(1) Since the ratio of efficiency of one men is 50% of that of one girl. 1y = 2b --------(2) From equations (1) and (2): 2x = 3y = 6b The ratio of time taken by 1 boy, 1 girl and 1 men alone to complete work: 2: 3: 6 Let the time taken by 1 boy, 1 girl and 1 men alone to complete the work be ‘2p’, ‘3p’ and ‘6p’ days respectively. So, (1/2p) + (1/3p) + (1/6p) = 1/5 p = 5 Time taken by 1 boy alone to complete the work = 2 × 5 = 10 days
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