Question : A is 40% more efficient than B. How much time will they take to work together to complete a job which A alone could have done in 31 days?
Option 1: $\frac{217}{12}\ \text{days}$
Option 2: $\frac{515}{32}\ \text{days}$
Option 3: $\frac{215}{12}\ \text{days}$
Option 4: $\frac{517}{32}\ \text{days}$
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Correct Answer: $\frac{217}{12}\ \text{days}$
Solution :
Given: A is 40% more efficient than B.
The time taken by A to complete the task alone is 31 days.
Work = Time × Efficiency.
Let B's efficiency be 100.
Then, $\frac{A}{B} = \frac{140}{100}$
⇒ $\frac{A}{B} = \frac{7}{5}$
The total work is done by A in 31 days.
Let the total work = 31 × 7 = 217 units
So, the time taken with A and B working together $=\frac{217}{7+5}=\frac{217}{12}$ days
Hence, the correct answer is $\frac{217}{12}\ \text{days}$.
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