Avni and Beena started a business by investing Rs. $P$ and Rs. $1.2P$ respectively. After $x$ months, Avni withdrew her entire investment and Chetna joined the business. At the end of 9 months, Beena increased her initial investment by 25%. On completion of one year, the combined share of Avni and Beena in the total profit was Rs. 14,200. If Beena had increased her investment after $x$ months, the ratio of Avni's to Beena's share in the total profit would have been $10 : 27$.

**If the ratio of their profit shares was $20 : 51$, what is the difference between the profit shares of Avni and Beena?**

Question

Avni and Beena started a business by investing Rs. $P$ and Rs. $1.2P$ respectively. After $x$ months, Avni withdrew her entire investment and Chetna joined the business. At the end of 9 months, Beena increased her initial investment by 25%. On completion of one year, the combined share of Avni and Beena in the total profit was Rs. 14,200. If Beena had increased her investment after $x$ months, the ratio of Avni's to Beena's share in the total profit would have been $10 : 27$.

**If the ratio of their profit shares was $20 : 51$, what is the difference between the profit shares of Avni and Beena?**

Accepted Answer

**Solution:**

1. Let the profit shares of Avni and Beena be $20a$ and $51a$ respectively.

2. According to the problem, their combined profit share is Rs. 14,200:
   
   $$20a + 51a = 14200$$

3. Simplify to find $a$:
   
   $$71a = 14200 \ a = \frac{14200}{71} = 200$$

4. The difference between their profit shares is:
   
   $$51a - 20a = 31a = 31 	imes 200 = 6200$$

**Answer:** Rs. 6200

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