Question

A can do a work at the same time in which B and C together can do it. If A and B together could do the work in 10 days and C alone can do the same work in 50 days, then how many days will B alone take?

1. 25 days
2. 35 days
3. 40 days
4. 30 days

Answer 1

Correct Answer - Option 1 : 25 days

Given:

A and B together takes = 10 days

C alone takes = 50 days

B and C together takes = Time take by A alone

Calculation:

(A + B)’s 1 day’s work = 1/10

C’s 1 day’s work = 1/50

∴ (A + B + C)’s 1 day’s work = 1/10 + 1/50

⇒ 6/50

⇒ 3/25      ----(i)

A’s 1 day’s work = (B + C)’s 1 day’s work      ----(ii)

From (i) and (ii), we get: 2 × (A’s 1 day’s work) = 3/25

∴ A’s 1 day’s work = 3/50

∴ B’s 1 day’s work = (1/10 – 3/50)

⇒ 2/50

⇒ 1/25

∴ B alone will take 25 days to do the work.