Question : A is three times as good a worker as B and therefore can finish a job in 40 days less than B. Working together, they can do it in:
Option 1: 14 days
Option 2: 13 days
Option 3: 20 days
Option 4: 15 days
Correct Answer: 15 days
Solution :
The time is inversely proportional to the efficiency
The ratio of efficiency of A and B = 3 ∶ 1
⇒ The ratio of time taken by A and B = 1 ∶ 3
Let the time taken by A and B be $x$ and $3x$
According to the question, we have
Time difference to taken by A and B = 40 days
$3x - x = 40$
$⇒ x = 20$ days
Now,
A can complete the whole work in 20 days.
So, A's one-day work = $\frac{1}{20}$
B can complete the whole work in 60 days.
So, B's one-day work = $\frac{1}{60}$
Now,
One day work of A and B together $= \frac{1}{20}+\frac{1}{60}$
$= \frac{3+1}{60}$
$ = \frac{4}{60} = \frac{1}{15}$
∴ The time taken by A and B together is 15 days.
Hence, the correct answer is 15 days.
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