A can complete a piece of work in 60 days. He worked for 15 days and B finished the remaining work in 30 days. If they work together then the work will be completed in:

Correct option is D

Given:
A's total time to complete work alone: 60 days
A worked for: 15 days
B completed the remaining work in: 30 days
Solution:
A's work rate=$$\frac{1}{60}$$​ per day.
Work done by A:
$$15 \times \frac{1}{60} = \frac{15}{60} = \frac{1}{4}$$​ (25% of the work)
Remaining work
​$$= 1 - \frac{1}{4} = \frac{3}{4}$$​ (75% of the work)

B completes $$\frac{3}{4}$$​ of the work in 30 days.

B's work rate:$$\frac{\frac{3}{4}}{30} = \frac{3}{120} = \frac{1}{40} \text{ per day}$$​​
Total work rate when A and B work together:
$$\frac{1}{60} + \frac{1}{40} = \frac{2 + 3}{120} = \frac{5}{120} = \frac{1}{24} \text{ per day}$$​​

Time required:

$$\frac{1}{\frac{1}{24}} = 24 \text{ days}$$​​
Alternate Method :
Assume total work = LCM of 60 and 30 = 60 units.
A's work rate =$$\frac{60}{60}$$​= 1 unit/day.
A's work in 15 days=$$15 \times 1$$​= 15  units.
Remaining work = 60 - 15 = 45 units.
B's work rate $$= \frac{45}{30}$$​ = 1.5 units/day.
Combined rate = 1 + 1.5 = 2.5  units/day.
Time together =$$\frac{60}{2.5} = 2$$​4 days.