Question
Download Solution PDFA works 3.5 times as fast as B, and A takes 45 days less than B to complete a job when each works alone. Calculate the number of days taken to complete the same job if A and B work together.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
A works 3.5 times as fast as B
A takes less days to complete the work than B = 45
Formula Used
Efficiency = 1/Time [When work is same]
Calculation:
The ratio of efficiency of A and B = 7 : 2
The ratio of time of A and B = 2 : 7
Let us assume the time taken by A and B is 2x and 7x.
The difference in the number of days A and B = 45
⇒ 7x - 2x = 45
⇒ x = 45/5 = 9
So, Total Work = 9 × 14 = 126 units
Work completed by A and B in days = 126/9 = 14 days
∴ The required answer is 14 days.
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