Question

A can do a piece of work in 6 hours, B and C together can do it in 2 hours, while A and C together can do it in 3 hours. How long will B alone take to do it?
1. 1 hours 
2. 5 hours 
3. 3 hours 
4. 4 hours 
5. None of these 

Answer 1

Correct Answer - Option 3 : 3 hours 

Given:

A can do a piece of work in 6 hours

B and C together can do it in 2 hours

Formula:

(A + B + C)’s 1 day = 1/A + 1/B + 1/C

Calculation:

A can do a piece of work in 6 hours

A’s one hour work = 1/6

B and C together can do it in 2 hours

(B + C)'s one-hour work = 1/2

A and C together can do it in 3 hours

(A + C)'s one-hour work = 1/3
(A + B + C)’s 1 hour work = 1/6 + 1/2 = 8/12 = 2/3

B’s 1 hour work = 2/3 – 1/3 = 1/3

∴ B alone will take 3 hours to do the work.