Question
Pawan is able to finish
1/3rd of a task in 10 days. Qureshi, on the other hand, can complete the entire task in half the time Pawan would need to complete the full task. When Pawan, Qureshi, and Raju work together, they can finish the entire task in 8 days. How many days would it take for Raju to complete the entire task on his own?Solution
ATQ, Pawan can complete 1/3rd of a task in 10 days Therefore, Pawan can complete the whole task in 10 × 3 = 30 days. Therefore, Qureshi will complete the task in 30/2 = 15 days Let Raju takes 'd' days to complete the whole task alone. Let, the total task be 30d (L.C.M of 15, 30 and d) Efficiency of Pawan = 30d/30 = d unit/day Efficiency of Qureshi = 30d/15 = 2d unit/day Efficiency of Raju = 30d/d = 30 unit/day According to the question, 30d/(30 + 3d) = 8 Or, 30d = 24d + 240 Or, 6d = 240 Or, d = 40 days
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