Select the correct answerA takes 10 days less than the time taken by B to finish a piece of work. If both A and B can do it in 12 days, then the time taken by B alone to finish the work is?Options27 days30 days20 days25 days

Let's solve this step by step:

1. A and B together can finish the work in 12 days. So, their combined rate of work is 1/12 of the work per day.

2. According to the problem, A takes 10 days less than B to finish the work. Let's say B takes 'x' days to finish the work. Then A takes 'x-10' days to finish the work.

3. The rate of work of A is 1/(x-10) and the rate of work of B is 1/x.

4. Since they can together finish the work in 12 days, their combined rate of work is the sum of their individual rates of work. So, we have the equation:

   1/(x-10) + 1/x = 1/12

5. Solving this equation for 'x' will give us the time taken by B alone to finish the work.

6. Multiply the entire equation by 12x(x-10) to clear the denominators:

   12x + 12(x-10) = x(x-10)

7. Simplify the equation:

   12x + 12x - 120 = x^2 - 10x

8. Rearrange the terms:

   x^2 - 34x + 120 = 0

9. This is a quadratic equation in the form ax^2 + bx + c = 0. Solve for 'x' using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / 2a:

   x = [34 ± sqrt((34)^2 - 41120)] / 2*1 x = [34 ± sqrt(1156 - 480)] / 2 x = [34 ± sqrt(676)] / 2 x = [34 ± 26] / 2

10. We get two solutions: x = 30 and x = 4. But x cannot be 4 because then A would take 'x-10' = -6 days, which is not possible.

So, the time taken by B alone to finish the work is 30 days. Therefore, the correct answer is "30 days".