Raj and Priya started a business with ₹1,50,000 and ₹1,20,000 respectively. After 6 months, Priya invested an additional ₹60,000 and Raj withdrew ₹30,000. What is their profit-sharing ratio at the end of 1 year?

Correct Answer: Option 9:10

To find the profit-sharing ratio between Raj and Priya at the end of 1 year (12 months), we need to calculate the total equivalent investment made by each person over the 12-month period.

Profit-sharing ratio is calculated as:
Ratio = Total Investment of Raj : Total Investment of Priya

Step 1: Calculate Raj's total investment for 12 months
- For the first 6 months, Raj's investment was ₹1,50,000.
- After 6 months, Raj withdrew ₹30,000. So, his remaining investment for the next 6 months was:
₹1,50,000 - ₹30,000 = ₹1,20,000.

Raj's equivalent 1-month investment:
$(150000\times 6)+(120000\times 6)$

$=900000+720000=1620000$

Step 2: Calculate Priya's total investment for 12 months
- For the first 6 months, Priya's investment was ₹1,20,000.
- After 6 months, Priya invested an additional ₹60,000. So, her new investment for the next 6 months was:
₹1,20,000 + ₹60,000 = ₹1,80,000.

Priya's equivalent 1-month investment:
$(120000\times 6)+(180000\times 6)$

$=720000+1080000=1800000$

Step 3: Determine the profit-sharing ratio
Ratio of Raj : Priya = 1,620,000 : 1,800,000

Dividing both sides by 180,000:
$\frac{1620000}{180000}:\frac{1800000}{180000}=9:10$

Thus, their profit-sharing ratio at the end of 1 year is 9:10.