X and Y started a business investing Rs. 60,000 and Rs. 90,000 respectively. After 5 months, X withdrew half his capital, and Y added Rs. 30,000 more.

Initial investments:
X = Rs. 60,000
Y = Rs. 90,000

First 5 months

X: $60000 \times 5 = 300000$
Y: $90000 \times 5 = 450000$

After 5 months

X withdraws half → remaining = Rs. 30,000
Y adds Rs. 30,000 → new capital = Rs. 1,20,000

Next 7 months

X: $30000 \times 7 = 210000$
Y: $120000 \times 7 = 840000$

Total capital × time

X: $300000 + 210000 = 510000$
Y: $450000 + 840000 = 1290000$

Ratio of profit:

$510000 : 1290000$

Divide by 30000:

$17 : 43$

Total parts = $17 + 43 = 60$

Total profit = Rs. 49,500

X's share:

$49500 \times \frac{17}{60}$

$= 825 \times 17$

$= 14025$

X's share = Rs. 14,025