A, B and C enter into a partnership and their shares are in the ratio \( \frac{1}{4} : \frac{1}{3} : \frac{1}{4} \). After \(2\) months, A withdraws half of his capital and after \(10\) months a profit of ₹\(378\) is divided among them. What is B's share? A, B এবং C একটি অংশীদারি ব্যবসায় প্রবেশ করে এবং তাদের মূলধনের অনুপাত \( \frac{1}{4} : \frac{1}{3} : \frac{1}{4} \)। \(2\) মাস পরে A তার মূলধনের অর্ধেক তুলে নেয় এবং \(10\) মাস পরে মোট লাভ ₹\(378\) তাদের মধ্যে ভাগ করা হয়। B-এর লাভের অংশ কত?

Let the initial capitals be proportional to

\[ \frac{1}{4} : \frac{1}{3} : \frac{1}{4} \]

Taking LCM \(=12\):

\[ 3 : 4 : 3 \]

Thus initial capitals:

A = \(3\), B = \(4\), C = \(3\)

For A:

First \(2\) months:

\[ 3 \times 2 = 6 \]

After withdrawing half, capital becomes \(1.5\) for remaining \(8\) months:

\[ 1.5 \times 8 = 12 \]

Total for A:

\[ 6 + 12 = 18 \]

For B:

\[ 4 \times 10 = 40 \]

For C:

\[ 3 \times 10 = 30 \]

Thus the ratio of profit:

\[ 18 : 40 : 30 \]

Simplifying:

\[ 9 : 20 : 15 \]

Total parts:

\[ 9 + 20 + 15 = 44 \]

B's share:

\[ \frac{20}{44} \times 378 \]

\[ = 171.82 \]

Correct Option: B