Question
Download Solution PDFA and B each can do a work in 75 days. They began the work together but A left after some time and B completed the remaining work in 23 days. After how many days of the start of the work did A leave ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A and B each can do a work in 75 days.
B completed the remaining work in 23 days.
Formula used:
Work done by A and B per day = \(1/75 + 1/75 = 2/75\)
Work done by B in 23 days = \(23 × 1/75\)
Calculation:
Let A worked for x days.
Work done by A and B together in x days = \(x × 2/75 \)
Work done by B alone in 23 days = \(23 × 1/75 = 23/75\)
Total work = 1
⇒ \(x × 2/75 + 23/75 = 1\)
⇒ \(x × 2/75 = 1 - 23/75\)
⇒ \(x × 2/75 = 52/75\)
⇒ x = \( 52/75 × 75/2\)
⇒ x = 26
∴ The correct answer is option (3).
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