Question

A works twice as fast as B. If B can complete a piece of work independently in 12 days, then what will be the number of days taken by A and B together to finish the work?

• A. 4
• B. 6
• C. 8
• D. 18

Hint:

If A is k times as efficient as B, A's time = B's time / k.

Answer 1

The Correct Option is A

To solve this problem, we need to determine how many days A and B together will take to complete a piece of work. Let's proceed step by step:

1. B can complete the work in 12 days. Therefore, B’s work rate is \(\frac{1}{12}\) of the work per day.
2. A works twice as fast as B. Hence, A’s work rate is \(2 \times \frac{1}{12} = \frac{1}{6}\) of the work per day.
3. When A and B work together, their combined work rate is the sum of their individual work rates: \(\frac{1}{6} + \frac{1}{12}\).
   • To find the sum, we need a common denominator. The least common multiple of 6 and 12 is 12.
   • Convert \(\frac{1}{6}\) to a denominator of 12: \(\frac{1}{6} = \frac{2}{12}\).
   • Add the fractions: \(\frac{2}{12} + \frac{1}{12} = \frac{3}{12} = \frac{1}{4}\).
4. The combined work rate of A and B is \(\frac{1}{4}\) of the work per day, meaning they can complete the entire work in 4 days.

Thus, the number of days taken by A and B together to finish the work is 4 days.