Question : A 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.
Option 1: 10.5
Option 2: 17.5
Option 3: 21
Option 4: 14
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Correct Answer: 14
Solution :
The ratio of the number of days A and B take to complete the work alone is in the inverse ratio of their efficiencies.
$\therefore$ The ratio of the number of days taken by A and B $ = 1 : 3.5$
Let the number of days be $x$ and $3.5x$.
The difference in the number of days = $3.5x-x=2.5x$
According to the question,
$2.5x = 45$
$\therefore x=\frac{45}{2.5} = 18$
Number of days taken by A = 18
Number of days taken by B = 18 × 3.5 = 63
Work done by A and B in 1 day = $\frac{1}{18} + \frac{1}{63} = \frac{1}{14}$
So, together they will complete the work in 14 days.
Hence, the correct answer is 14 days.
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