Question

Lalita borrowed some money from Praveen at the interest rate of 10% per annum.she repaid her debt by paying rupees 13500 after 1 year 3 months.what was the sum of money borrowed by lalit.?

Answer 1

Given :

Total Amount : ₹13500

Rate of interest : 10%

Time : 1 year 3 months

To find :

The sum (principle) borrowed by Lalita.

Solution :

First, we should find the simple interest.

Simple interest :

$\sf \dashrightarrow SI = \dfrac{P \times R \times T}{100}$

$\sf \dashrightarrow \dfrac{P \times 10 \times 5}{100 \times 4}$

$\sf \dashrightarrow \dfrac{P \times 1 \times 5}{10 \times 4}$

$\sf \dashrightarrow \dfrac{P \times 1}{2 \times 4}$

$\sf \dashrightarrow \dfrac{P}{8}$

Now, we'll find the value of principle by the formula of total amount.

$\sf \dashrightarrow Total \: Amount = Principle + Simple \: Interest$

$\sf \dashrightarrow 13500 = P + \dfrac{P}{8}$

$\sf \dashrightarrow 13500 = \dfrac{8P + P}{8}$

$\sf \dashrightarrow 13500 = \dfrac{9P}{8}$

$\sf \dashrightarrow \dfrac{9P}{8} = 13500$

$\sf \dashrightarrow 9P = 13500 \times 8$

$\sf \dashrightarrow 9P = 108000$

$\sf \dashrightarrow P = \dfrac{108000}{9}$

$\sf \dashrightarrow P = 12000$

Hence, the principle amount borrowed is ₹12000.