'Asmita,' who is three times as efficient as 'Bittu,' can complete a task on her own in 15 days. 'Asmita' and 'Bittu' began working together, but after 3 days, 'Asmita' departed, and 'Chinky,' who is 25% less efficient than 'Bittu,' took over. 'Bittu' left the job 2 days before its completion, and 'Chinky' completed the remaining work alone. Determine the number of days 'Bittu' and 'Chinky' worked together.

Solution

ATQ, Since, ‘Asmita’ is thrice as efficient as ‘Bhanu’. Therefore, time taken by ‘Bhanu’ to complete the whole work alone = 3 × 15 = 45 days Let total amount of work = 45 units {LCM of 15 and 45} Efficiency of ‘Asmita’ = 45/15 = 3 units/day Efficiency of ‘Bhanu’ = 45/45 = 1 unit/day Efficiency of ‘Chinky’ = 0.75 units/day Amount of work completed by ‘Asmita’ and ‘Bhanu’ together in the first 3 days = 3 × (1 + 3) = 12 units Amount of work completed by ‘Chinky’ alone in 2 days = 2 × 0.75 = 1.5 units Remaining work = 45 – 12 – 1.5 = 31.5 units Therefore, time taken for which ‘Bhanu’ and ‘Chinky’ worked together  = {31.5/(1 + 0.75)} = 18 days