A and B complete a work in 20 days. If A alone can do it in 45 days, then B alone can do one-third of the same work in ______________ days.​

Correct option is B

Given:

A and B together complete the work in 20 days.

A alone can complete the work in 45 days.

Solution:

Rate of B = $$\frac{1}{20} - \frac{1}{45}$$​​

​$$= \frac{45 - 20}{20 \times 45}\\ \ \\ = \frac{25}{900} = \frac{1}{36}$$​​

This means B completes the work in 36 days

Time taken by B to complete one-third of the work:

Time = $$\frac{1}{3} \times 36 = 12 \text{ days}$$ 

Alternate Solution: ​

Total work = LCM of 45 and 20 = 180 

Work rate of A = $$\frac{180}{45}$$​ =4 units/day

Work rate of A and B together = $$\frac{180}{20}$$​ = 9 units/day

Work rate of B = 9 - 4 = 5 units/day

Time taken by B to complete one-third of the work( 180$$\times\frac 13$$ = 60)

Time = $$\frac{60}{5}$$​ = 12 days