Question
Download Solution PDFA does half as much work as B in three-fourth of the time. If together they take 66 days to complete the work, how many days shall B alone take to do it?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A does half as much work as B in three-fourth of the time.
Together they complete the work in 66 days.
Formula Used:
Total Work = Efficiency × Time
Calculation:
Assume:
B completes the work in x days.
A does half the work in 3/4 of the time ⇒ A does full work in (3/4) × 2 = 3x/2 days.
Work done by A in one day = 1 / (3x/2) = 2 / 3x
Work done by B in one day = 1 / x
Together, work done in one day = 1 / 66
⇒ (2 / 3x) + (1 / x) = 1 / 66
⇒ (2 + 3) / 3x = 1 / 66
⇒ 5 / 3x = 1 / 66
⇒ 3x = 5 × 66 = 330
⇒ x = 330 / 3 = 110
∴ B alone can complete the work in 110 days.
Last updated on Jul 8, 2025
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