Question
‘Pawan’, ‘Qureshi’, and
‘Ram’ can finish 50%, 1/3, and 3/4 of a job in 24, 18, and 54 days, respectively. If ‘Pawan’ and ‘Qureshi’ start the job together and work on it for 18 days, calculate how long ‘Ram’ will take to complete the remaining work alone.Solution
ATQ, Time taken by ‘Pawan’ to complete the whole work = (24/0.50) = 48 days Time taken by ‘Qureshi’ to complete the whole work = 18 × (3/1) = 54 days Time taken by ‘Ram’ to complete the whole work = 54 × (4/3) = 72 days Let total work be 432 units {LCM of 48, 54, and 72} Efficiency of ‘Pawan’ = (432/48) = 9 units/day Efficiency of ‘Qureshi’ = (432/54) = 8 units/day Efficiency of ‘Ram’ = (432/72) = 6 units/day Amount of work done by ‘Pawan’ and ‘Qureshi’ together in 18 days = (9 + 8) × 18 = 306 units Remaining work = (432 – 306) = 126 units So, required time taken by ‘Ram’ = (126/6) = 21 days
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