Question
'Aman' and 'Bittu' alone can do some work in 30 days and
45 days, respectively. They work together for eleven days after which both 'Aman' and 'Bittu' are replaced by 'Charu' and 'Danny'. 'Charu' is twice as efficient as 'Bittu' and also their combined efficiency is same as that of 'Aman' and 'Danny'. Determine the time taken by 'Charu' and 'Danny' to finish the remaining work.Solution
ATQ. Let Aman, Bittu, Charu and Danny be defined as A, B, C and D respectively. Let the total work be 90 units. {LCM (30 and 45) } So, efficiency of 'A' = 90 ÷ 30 = 3 units/day And efficiency of 'B' = 90 ÷ 45 = 2 units/day And efficiency of 'C' = 2 X 2 = 4 units/day ATQ, Combined efficiency of 'A' and 'D' = Combined efficiency of 'B' and 'C' = 4 + 2 = 6 units/day So, efficiency of 'D' = 6 - 3 = 3 units/day Work done by 'A' and 'B' in 11 days = 11 X (3 + 2) = 55 units And work done by 'C' and 'D' = 90 - 55 = 35 units So, time taken by 'C' and 'D' to finish the remaining work = 35 ÷ (3 + 4) = 5 days
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