A and B complete a work in 15 days. If A alone can do it in 17 days, then B alone can do two-third of the same work in ______________ days.​

Correct option is A

Given:

A + B together finish the work in 15 days

A alone finishes it in 17 days

Formula Used:

Rate = $$\frac1 { Time}$$​

Solution:

Let B alone finish the whole work in b days.

​$$\frac{1}{15} = \frac{1}{17} + \frac{1}{b}$$​​

​$$\frac{1}{b} = \frac{1}{15} - \frac{1}{17} = \frac{17 - 15}{255} = \frac{2}{255}$$​​

​$$b = \frac{255}{2} = 127.5 \text{ days (whole work)}$$​​

Two-thirds of the work:

​$$\frac{2}{3} \times 127.5 = 85 \text{ days}$$​​

Alternate Solution:

Total work =  LCM of 15 and 17 = 255 units of work

Rates:

A + B: $$\frac{255}{15}$$​ = 17 units/day

A alone: $$\frac{255}{17}$$​ = 15 units/day

B’s rate = 17 - 15 = 2 units/day

Whole work time for B

​$$\frac{255}{2} = 127.5 \text{ days}$$​​

Two-thirds of the work

​$$\frac{2}{3} \times 127.5 = 85 \text{ days}$$​​