Correct Answer - Option 2 :
\(7\frac{1}{2}\) days
Given:
A can complete a work in 12 days.
B can complete a work in 8 days
Concept Used:
Total units of work is equal to the LCM of number of days required to complete the work.
Efficiency = Total units of work/Number of days taken
Calculation:
Total units of work, LCM of 12 and 8
Total units of work,
⇒ 24 units
Efficiency of A,
⇒ 24/12
⇒ 2 units/day
Efficiency of B,
⇒ 24/8
⇒ 3 units/day
B worked for 3 days and left,
Total units of work completed by B in 3 days,
⇒ 3 × 3
⇒ 9 units
Remaining units of work completed by A,
⇒ Remaining units of work = 24 – 9
⇒ Remaining units of work = 15 units
Time taken to complete the work,
⇒ 15/2
⇒ \(7\frac{1}{2}\) days
∴ A can complete the remaining work in \(7\frac{1}{2}\) days.