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.