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Avni and Beena started a business by investing ₹P and ₹1.2P respectively. After x months, Avni withdrew her entire amount and Chetna entered the business. After 9 months, Beena increased her initial investment by 25%. At the end of one year, the share of Avni and Beena in the total profit was ₹14,200. If Beena had increased her investment after x months, then the ratio of the share of Avni and Beena in the total profit would have been 10:27. If a person invested ₹1.2P at 2.5x% annual simple interest rate for x years and received total interest of ₹6,480, find P.

1. 5400
2. 8000
3. 7200
4. 6000

Correct answer: 6000

Solution

In partnership, profit share is proportional to capital multiplied by time. Using the two different timing conditions gives a value of x, and then the simple interest relation = PRT/100 can be used with the given rate 2.5x% and time x years. Solving these equations yields P = 6000.

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