A and B can do a piece of work in 25 days and 30 days, respectively. They worked together for 6 days, after while B was replaced by P and the work was finished in the next 8 days. How long will P alone take to complete the same work?

Correct option is C

​
Given:
A's 1 day work = $$\frac 1{25}$$​​

B's 1 day work = $$\frac1{30}$$​​
They worked together for 6 days.
Then A and P worked for 8 days to finish the remaining work.
Formula Used:
Work = Rate × Time
Total Work = 1 unit (assuming whole work as 1)
Solution:
Work done by A and B in 6 days = 6 × ($$\frac1{30} + \frac1{25}$$​)   $$= 6 \times \frac{11}{150} = \frac{66}{150}$$​​
Remaining work = $$1 - \frac{66}{150} = \frac{84}{150}$$​​
Let P's 1 day work be $$\frac 1x$$​
Work done by A and P in 8 days = $$8 \times \left( \frac{1}{25} + \frac{1}{x} \right) = \frac{84}{150}$$​​
​$$\Rightarrow 8 \times \left( \frac{1}{25} + \frac{1}{x} \right) = \frac{84}{150}\\\ \\\Rightarrow \frac{1}{25} + \frac{1}{x} = \frac{84}{150 \times 8} = \frac{84}{1200}\\\ \\\Rightarrow \frac{1}{x} = \frac{84}{1200} - \frac{1}{25}\\\ \\\Rightarrow \frac{1}{x} = \frac{84 - 48}{1200} = \frac{36}{1200} = \frac{3}{100}\\\ \\\Rightarrow x = \frac{100}{3} = 33 \frac 13 \text {days}\\\ \\$$​​
Therefore, P alone can complete the work in $$33 \frac 13 \text {days}$$