A and B can do a piece of work in 12 days. B and C together can do it…

The correct answer is Option (2) → 20 days

Let the daily work rates of A, B, C be $a, b, c$ respectively.

Given:

• $a + b = \frac{1}{12}$​ …(1)
• $b + c = \frac{1}{15}$​ …(2)
• A is twice as good as C → $a = 2c$

Substitute $a = 2c$ into (1):

$2c + b = \frac{1}{12} \quad …(3)$

From (2):

$b = \frac{1}{15} – c$

Substitute into (3):

$2c + \left(\frac{1}{15} - c\right) = \frac{1}{12}$

$c + \frac{1}{15} = \frac{1}{12}$

$c = \frac{1}{12} - \frac{1}{15}$

LCM of 12 and 15 = 60:

$c = \frac{5 - 4}{60} = \frac{1}{60}$

So:

$a = 2c = \frac{2}{60} = \frac{1}{30}$

Now find b:

$b = \frac{1}{15} - \frac{1}{60} = \frac{4 - 1}{60} = \frac{3}{60} = \frac{1}{20}$

Time taken by B alone:

$= \frac{1}{b} = 20 \text{ days}$