A and B can separately do a piece of work in \(20\) days and \(15\) days, respectively. They worked together for \(6\) days, after which B was replaced by C. The work was finished in the next \(4\) days. The number of days in which C alone could do the work is: A এবং B আলাদাভাবে একটি কাজ যথাক্রমে \(20\) দিন ও \(15\) দিনে করতে পারে। তারা একসঙ্গে \(6\) দিন কাজ করার পর B-এর পরিবর্তে C কাজ শুরু করে। পরবর্তী \(4\) দিনে কাজ শেষ হয়। C একা কাজটি কত দিনে করতে পারবে?

Rate of A = \[ \frac{1}{20} \]

Rate of B = \[ \frac{1}{15} \]

Work done by A and B together in \(6\) days:

\[ 6\left(\frac{1}{20} + \frac{1}{15}\right) \]

LCM of \(20\) and \(15\) is \(60\):

\[ 6\left(\frac{3 + 4}{60}\right) = 6\left(\frac{7}{60}\right) = \frac{42}{60} = \frac{7}{10} \]

Remaining work:

\[ 1 - \frac{7}{10} = \frac{3}{10} \]

Now A and C finish \(\frac{3}{10}\) work in \(4\) days.

So their one-day work:

\[ \frac{3}{10} \div 4 = \frac{3}{40} \]

Thus,

\[ \frac{1}{20} + C = \frac{3}{40} \]

\[ \frac{1}{20} = \frac{2}{40} \]

\[ C = \frac{3}{40} - \frac{2}{40} = \frac{1}{40} \]

Therefore, C alone can do the work in:

\[ 40 \text{ days} \]

Correct Answer: C