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Dinesh divided Rs.88400 between his son and a daughter in such a way that the amount his son receives at the end of 7 years is equal to the amount his daughter receives at the end of 9 years, rate of compound interest being 10% per annum. How much money has he deposited in the bank (in Rs.) in the name of his daughter?

Dinesh divided Rs.88400 between his son and a daughter in such a way that the amount his son receives at the end of 7 years is equal to the amount his daughter receives at the end of 9 years, rate of compound interest being 10% per annum. How much money has he deposited in the bank (in Rs.) in the name of his daughter? Correct Answer 40000

Given:

Rate = 10%

Amount = 88400

Formula used:

Amount(A) = Principal(P)(1 + Rate(R)/100)Time(t)

Calculation:

Let the principal of son be x, and daughter be (88400 - x)

Amount of son for 7 years = Amount of daughter of 9 years at same rate 

⇒ x(1 + 10/100)7 = (88400 - x)(1 + 10/100)9

⇒ x/(88400 - x) = (1 + 10/100)2

⇒ x/(88400 - x) = 11 × 11/100

⇒ 100 x = 121(88400 - x)

⇒ 221x = 121 × 88400

⇒ x = 48400

Daughter amount = 88400 - 48400

⇒ 40000

∴ The daughter deposit amount is Rs 40000.

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