Harsh, Madhu and Anshu can complete a piece of work in 90, 60 and 45 days respectively. After working for x days together, Harsh left. After y more days Madhu left and Anshu completed the remaining work. Had Madhu not left they could have completed the work in (y + 4) days after Harsh had left. Had none of them left, then they would have completed the work in x + 7 days. Find the value of x + y.
Explanation:
Let the total work to be done = LCM (90, 60, 45) = 180 units.
Efficiency of Harsh = 2 units/day Efficiency of Madhu = 3 units/day Efficiency of Anshu = 4 units/day
Case 1: Had none of them left, then they would have completed the work in x + 7 days All three worked for (x + 7) days
⇒ Total work done = (x + 7) × (2 + 3 + 4) = 9(x + 7) ⇒ 9x + 63 = 180 ⇒ 9x = 117 ⇒ x = 13 days
Case 2: After working for x days together, Harsh left. Had Madhu not left they could have completed the work in (y + 4) days after Harsh had left Harsh worked for x days Madhu and Anshu worked for (x + y + 4) days
⇒ Total work done = 2x + (x + y + 4) × (3 + 4) = 9x + 7y + 28 ⇒ 9 × 13 + 7y + 28 = 180 ⇒ 7y = 180 – 28 – 117 ⇒ 7y = 35 ⇒ y = 5 days.
∴ x + y = 13 + 5 = 18
Hence, option (b).
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