Question

Ram can complete a work in 16 days, Shyam in 24 days and Rohan in 32 days. They started working together but after 4 days Ram and Rohan quit the work and remaining work was completed by Shyam alone, find out for how many days did Shyam work alone.    
1. 5 
2. 8
3. 11
4. 15 

Answer 1

Correct Answer - Option 3 : 11

Given :

Ram can do the work in 16 days 

Shyam can do the work in 24 days 

Rohan can do the work in 32 days 

Concept used :

Total days to complete the work = Total work/Work done per day 

Calculations :

Total work = LCM of 16, 24 and 32 

⇒ 96 units 

Ram's per day work = 96/16 = 6 units 

Shyam's per day work = 96/24 = 4 units 

Rohan's per day work = 96/32 = 3 units

Ram, Shyam and Rohan per day work = 6 + 4 + 3 = 13 units

Their total work in 4 days = 4 × 13 = 52 units

Remaining work = 96 - 52 = 44 units 

Days taken by Shyam to complete the remaining work = 44/4 

⇒ 11 

∴ Shyam work alone for 11 days to complete the remaining work