Correct Answer - Option 4 :
\(7\dfrac{1}{2}\) days
Given:
A person A can do a work = 20 days
Work done by A = 5 days
Remaining work done by B = 9 days
Calculation:
Part of work done by A = 5/20 = 1/4
⇒ Remaining work = 1- 1/4 = 3/4
⇒ The remaining (3/4)th work done by B in 9 days so
⇒ Time is taken by B to do complete work = 9 × 4/3 = 12 days
⇒ Let total work 60 unit (LCM of 12, 20)
⇒ The efficiency of A = Total work/time taken by A
⇒ The efficiency of A = 60/20 = 3
⇒ The efficiency of B = Total work/time taken by B
⇒ The efficiency of B = 20/12 = 5
⇒ Total efficiency of A and B = 3 + 5 = 8
⇒ Time is taken by A and B if they work together = 60/8 = 7.5 days
∴ A and B work together to finish work in 7.5 days.