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?

Correct Answer: Rs 7150

Step-by-Step Explanation:

Step 1: Understand the ratio of investments and time periods
Let the investment of Ritu be $I_1=7x$ and the investment of Priya be $I_2=8x$.
Ritu invested her money for 9 months ($T_1=9$).
Priya kept her money invested for the entire year, which is 12 months ($T_2=12$).

Step 2: Calculate the ratio of profit sharing
Profit is distributed according to the product of investment and time period ($\mathrm{Investment}\times \mathrm{Time}$).

$\text{Ratio of Profit (Ritu : Priya)}=\left(I_1\times T_1\right):\left(I_2\times T_2\right)$

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

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

Dividing both sides by 3x to simplify:

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

Step 3: Find the total ratio units and share of each
Total ratio units = $21+32=53$ units.
Total annual profit = Rs 34450.

Value of 1 ratio unit:

$\text{1 unit}=\frac{34450}{53}=650$

Step 4: Calculate the difference between their shares in profit
Difference in profit ratio units = $32-21=11$ units.

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

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