Question
Download Solution PDFP 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
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