Question

P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

Options

• `5 5/11`

• `5 6/11`

• `6 5/11`

• `6 6/11`

Answer 1

`5 5/11`

Explanation:

P can complete the work in (12 × 8) hrs = 96 hrs

Q can complete the work in (8 × 10) hrs = 80 hrs

∴ P's 1 hour's work = `1/96` and Q's 1 hour's work = `1/80`

(P + Q)'s 1 hour's work = `(1/96 + 1/80) = 11/480`

So, both P and Q will finish the work in `(480/11)` hrs

∴ Number of days of 8 hours each = `(480/11 xx 1/8) = 60/11` days = `5 5/11` days.