Question
Rohan can finish a task alone in 24 days. Shreya can do
50% of the same task alone in 12 days. If Shreya and Tanya work together, they can complete 60% of the task in 9 days. Find the time taken by Rohan and Tanya to finish the task together.Solution
ATQ, Time taken by Shreya to do the entire task = 12 ÷ 0.5 = 24 days Time taken by Shreya and Tanya to do the entire task together = 9 ÷ 0.6 = 15 days Let the total work be 120 units {LCM (24, 24, and 15)} So, the combined efficiency of Shreya and Tanya = 120 ÷ 15 = 8 units/day Efficiency of Shreya = 120 ÷ 24 = 5 units/day Efficiency of Tanya = 8 - 5 = 3 units/day Efficiency of Rohan = 120 ÷ 24 = 5 units/day So, required time taken = 120 ÷ (5 + 3) = 120 ÷ 8 = 15 days
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