Ritu and Priya invested in the ratio 7 : 8 in a business .They got an annual profit of Rs 34450. If Ritu withdrew her entire amount at the end of 9 months. Then find the difference between their share in profit?

The correct option is Rs 7150.

Step-by-step Explanation:

1. Understand the Investment Ratios and Time Durations:
Let the initial investment of Ritu be $7x$ and the initial investment of Priya be $8x$.
- Ritu invested her amount for $9$ months.
- Priya kept her investment in the business for the entire year, which is $12$ months.

2. Calculate the Ratio of Profits:
The ratio of profit sharing is calculated by taking the product of each person's investment and their respective investment duration (in months):

$\text{Profit Ratio}=(\text{Ritu's Investment}\times \text{Time}):(\text{Priya's Investment}\times \text{Time})$

$\text{Profit Ratio}=(7x\times 9):(8x\times 12)$

$\text{Profit Ratio}=63x:96x$

Simplifying the ratio by dividing both sides by $3x$:

$\text{Profit Ratio}=21:32$

3. Determine the Difference in Share of Profit:
Total ratio parts = $21+32=53$ parts.
Total annual profit = Rs 34,450.

The difference in parts between Priya's share and Ritu's share is:

$32-21=11\text{parts}$

Now, calculate the difference in profit share using the total profit:

$\text{Difference in Profit}=\frac{11}{53}\times 34450$

Dividing $34450$ by $53$:

$\frac{34450}{53}=650$

Now, multiply by $11$:

$\text{Difference in Profit}=11\times 650=7150$

Thus, the difference between their shares in profit is Rs 7150.