P and Q can complete a work alone in 18 days and 30 days respectively. They began the work together but P left the work after some days and Q completed the remaining work in 22 days. After how many days from the beginning P left the work?

Question

Question

This question was previously asked in

DFCCIL Executive CBT1 Electrical 25 Aug 2023 Shift 2 Official Paper

Answer 1

Given:

P can complete work in = 18 days

Q can complete work in = 30 days

Q completed remaining work in = 22 days

Formula Used:

Work done by P in 1 day = 1/18

Work done by Q in 1 day = 1/30

Calculations:

Work done by Q in 22 days = 22 × (1/30) = 22/30 = 11/15

Remaining work = 1 - 11/15 = 4/15

Work done by P and Q together in 1 day = 1/18 + 1/30

⇒ Work done by P and Q together in 1 day = (5 + 3) / 90 = 8/90 = 4/45

Let P left after x days.

Work done by P and Q together in x days = x × (4/45) = 4x/45

⇒ 4x/45 = 4/15

⇒ x = (4/15) × (45/4)

⇒ x = 3

∴ P left the work after 3 days from the beginning.