Question 54

A and B together borrowed a sum of ₹51,750 at an interest rate of 7%p.a. compound interest in such a way that to settle the loan, A paid as much amount after three years as paid by B after 4 years from the day of borrowing. The sum (in ₹) borrowed by B was:

Solution

let A borrow be Rs.x.

Borrowed by B = 51,750 - x

compound interest rate(r) = 7%

Amount paid by A after 3 year = amount paid by B after 4 year

Amount = $$principal(1 + r/100)^t$$

$$x(1 + 7/100)^3 = (51,750 - x)(1 + 7/100)^4$$

$$x = (51,750 - x) \times 107/100$$

100x = 5537250 - 107x

x = 5537250/207 = 26750

Borrowed by B = 51,750 - x = 51,750 - 26750 = 25000

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