Question
Deepak and Divya, alone can complete a work in 18 days and 27 days, respectively. They started the work together and left after 9 days such that the remaining work is completed by Dinesh alone in 9 days. If the total wage fixed for completing the work is Rs. 540, then find the share received by Dinesh.
Solution
Let total work = 54 units {LCM of 18 and 27} So, efficiency of ‘Deepak’ = (54/18) = 3 units/day Efficiency of ‘Divya’ = (54/27) = 2 units/day Amount of work done by Deepak in 9 days = 3 × 9 = 27 units Amount of work done by Divya in 9 days = 2 × 9 = 18 units Amount of work done by Dinesh = 54 – (27 + 18) = 9 units Ratio of amount of work done by Deepak, Divya and Dinesh = (27 : 18 : 9) = (3 : 2 : 1) Required wages of Dinesh = {1/(3 + 2 + 1)} × 540 = Rs. 90
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