Explanation:

- Vaibhav can complete the entire job in 60 days. So, he finishes \(\frac{1}{60}\) of the work per day.

- Vaibhav worked for 15 days, completing \(\frac{15}{60} = \frac{1}{4}\) of the work.

- The remaining work is \(\frac{3}{4}\), which Sandeep finishes in 30 days. Hence, Sandeep's work rate is \(\frac{3}{4} \div 30 = \frac{1}{40}\) per day.

- Together, Vaibhav and Sandeep's combined rate is \(\frac{1}{60} + \frac{1}{40}\).

- Finding a common denominator (120), we get \(\frac{2}{120} + \frac{3}{120} = \frac{5}{120} = \frac{1}{24}\).

- Hence, working together, they finish the work in 24 days.

Answer: Option 2 - 24 days