Question

A person A can do work in 20 days. He works for 5 days and stops doing the work. Then, a second person B completes the remaining work in 9 days. If A and B work together, how long will they take to complete the work?
1. 9 days
2. \(8\dfrac{1}{2}\) days
3. 8 days
4. \(7\dfrac{1}{2}\) days

Answer 1

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.