'Amit' and 'Bittu' alone can do some work in 24 hours

Solution

ATQ, Let the total work be 120 units. (LCM 24 and 20) So, efficiency of 'Amit' = (120/24) = 5 units/hour And efficiency of 'Bittu' = (120/20) = 6 units/hour For Statement I: Combined efficiency of 'Amit' and 'Charu' = {(120 X 0.6)/72} X 13 = 13 units/hour So, efficiency of 'Charu' = 13 - 5 = 8 units/hour So, time taken by 'Bittu' and 'Charu' to finish the whole work together = {(120)/(8 + 6)} = (60/7) hours So, statement I is true. For Statement II: Combined efficiency of 'Amit' and 'Charu' = {(120 X 0.6)/7.2} = 10 units/hour So, efficiency of 'Charu' = 10 - 5 = 5 units/hour So, time taken by 'Bittu' and 'Charu' to finish the whole work together = {(120)/(5 + 6)} = (120/11) hours So, statement II is false. For Statement III: Combined efficiency of 'Amit' and 'Charu' = {(120 X 0.6)/8} = 9 units/hour So, efficiency of 'Charu' = 9 - 5 = 4 units/hour So, time taken by 'Bittu' and 'Charu' to finish the whole work together = {(120)/(4 + 6)} = 12 hours So, statement III is true.