Question

Surya and Manoj can complete a work in 54 days if they work together. However, due to some reasons, Surya left the work 24 days before the completion of work, after that Manoj completed the remaining work in 96 days, then find in how many days Surya can complete the whole work if he works alone. 
1. 72
2. 108
3. 216
4. 144

Answer 1

Correct Answer - Option 1 : 72

Given :

Surya and Manoj can complete a work in 54 days if they work together. 

Surya left the work 24 days before the completion of the work. 

Concept used : 

Total work = work efficiency × Total time 

Calculation :

Total work = 54 units 

Surya and Manoj per day work = 54/54 

⇒ 1 unit 

Surya left the work 24 days before the completion.

So they worked together for 30 days    (54 - 24 = 30)

Work completed by them in 30 days = 30 × 1

⇒ 30 units 

Remaining work = 54 - 30 

⇒ 24 units 

Manoj can complete this remaining work in 96 days 

Manoj's per day work = 24/96 

⇒ (1/4) units 

Manoj per day work + Surya per day work = 1 unit 

Surya per day work = (3/4) unit 

Time taken by Surya to complete whole work (54 units) alone = 54/(3/4) 

⇒ 72 days 

∴ Option 1 will be the correct choice.