X and Y started a business by investing ₹60,000 and ₹90,000 respectively. After 6 months, X doubled his capital, while Y reduced his capital by ₹30,000. If the total annual profit is ₹62,000, what is Y's share(to the nearest integer)?

The correct option is ₹28,182.

To find Y's share of the total annual profit, we need to calculate the effective investment of both X and Y over the period of one year (12 months).

Step 1: Calculate X's total investment for 12 months
For the first 6 months, X invested ₹60,000.
After 6 months, X doubled his capital, so his new investment becomes:
$\mathrm{60,000}\times 2=\mathrm{1,20,000}$
This capital remained for the remaining 6 months.
Total effective investment of X for 1 year:
$=(\mathrm{60,000}\times 6)+(\mathrm{1,20,000}\times 6)$
$=\mathrm{3,60,000}+\mathrm{7,20,000}=\mathrm{10,80,000}$

Step 2: Calculate Y's total investment for 12 months
For the first 6 months, Y invested ₹90,000.
After 6 months, Y reduced his capital by ₹30,000, so his new investment becomes:
$\mathrm{90,000}-\mathrm{30,000}=\mathrm{60,000}$
This capital remained for the remaining 6 months.
Total effective investment of Y for 1 year:
$=(\mathrm{90,000}\times 6)+(\mathrm{60,000}\times 6)$
$=\mathrm{5,40,000}+\mathrm{3,60,000}=\mathrm{9,00,000}$

Step 3: Find the ratio of profit sharing between X and Y
Ratio of Investment (X : Y):
$=\mathrm{10,80,000}:\mathrm{9,00,000}$
Dividing both sides by 1,80,000:
$=6:5$

Step 4: Calculate Y's share in the total profit of ₹62,000
Sum of ratio parts = 6 + 5 = 11
Y's Share:
$=\frac{5}{11}\times \mathrm{62,000}$
$=\frac{\mathrm{3,10,000}}{11}$
$\approx \mathrm{28,181.818...}$

Rounding to the nearest integer, Y's share is ₹28,182.