Question
‘D’ and ‘E’ together can finish a task in 40
days, while ‘E’ and ‘F’ together can finish the same task in 30 days. ‘D’ and ‘E’ together worked on it for 35 days and then ‘F’ alone completed the remaining work in 10 days. If ‘D’, ‘E’, and ‘F’ started a certain task and worked together till its completion for which they received Rs. 1800 as total wage, then the share of ‘D’ out of the total wage will be:Solution
Let the total amount of work = LCM of 40 and 30 = 120 units Work done by ‘D’ and ‘E’ in one day = 120/40 = 3 units Work done by ‘E’ and ‘F’ in one day = 120/30 = 4 units Work done by ‘D’ and ‘E’ in 35 days = 35 × 3 = 105 units Remaining work = 120 - 105 = 15 units Efficiency of ‘F’ = 15/10 = 1.5 units per day Efficiency of ‘E’ = 4 - 1.5 = 2.5 units per day Efficiency of ‘D’ = 3 – 2.5 = 0.5 units per day Share of ‘D’ = (0.5 / (0.5 + 2.5 + 1.5)) × 1800 = Rs 200
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