Question

A and B, working together, can do a work in 8 days. If A alone can do the work in 12 days, then in how many days can B alone do 25 percent of the work?

• A. 5
• B. 6
• C. 7
• D. 4

Hint:

In work and time problems, first find the individual work rates, then use the relationship \( \text{Work} = \text{Rate} \times \text{Time} \) to solve for the unknown time.

Answer 1

The Correct Option is B

Let the total work be \( W \). - A and B together can complete the work in 8 days, so their combined work rate is: \[ \frac{1}{8} \, \text{of the work per day} \] - A alone can complete the work in 12 days, so A’s work rate is: \[ \frac{1}{12} \, \text{of the work per day} \] The work rate of B alone is the difference between their combined work rate and A’s work rate: \[ \text{B's work rate} = \frac{1}{8} - \frac{1}{12} = \frac{1}{24} \] To find how many days it will take B to do 25 percent of the work, we calculate: \[ \text{Days for B to do 25 percent work} = \frac{0.25 \, W}{\frac{1}{24} \, W} = 6 \, \text{days} \] Thus, the correct answer is \( \boxed{6} \) days.