Question

Mr Sharma borrowed some money from a friend at the interest rate of 8% per annum. He repaid his debt by paying rupees 16800 at the end of 5 years. How much did he borrow?

Answer 1

★ Solution :-

We know that, the amount is obtained when we add simple interest and principle. So, we can find the principle value by the same formula.

Principle :-

$\sf \leadsto Simple \: interest + Principle = Amount$

$\sf \leadsto \dfrac{P \times R \times T}{100} + Principle = Amount$

$\sf \leadsto \dfrac{P \times 8 \times 5}{100} + P = 16800$

$\sf \leadsto \dfrac{P \times 40}{100} + P = 16800$

$\sf \leadsto \dfrac{P \times 2}{5} + P = 16800$

$\sf \leadsto \dfrac{2P}{5} + P = 16800$

$\sf \leadsto \dfrac{2P + 5P}{5} = 16800$

$\sf \leadsto \dfrac{7P}{5} = 16800$

$\sf \leadsto 7P = 16800(5)$

$\sf \leadsto 7P = 84000$

$\sf \leadsto P = \dfrac{84000}{7}$

$\sf \leadsto P = 12000$

Therefore, the principle amount borrowed by Mr Sharma is ₹12000.

Answer 2

Given :

† Total Amount - ₹16800

† Rate of interest - 8%

† Time - 5 years

To Find :

† The money borrowed by Mr.Sharma.

Solution :

First, we should find the interest amount to be paid by him.

Let the principle amount be P.

According to the question,

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

$\sf :\implies\: \dfrac{P \times 8 \times 5}{100}$

$\sf :\implies\: \dfrac{P \times 40}{100}$

$\sf :\implies\: \dfrac{P \times 2}{5}$

$\sf :\implies\: \dfrac{2P}{5}$

Now, let's find the value of principle amount by the formula of total amount.

$\sf:\implies\: Amount = Principle + Simple \: Interest$

$\sf :\implies\: 16800 = P + \dfrac{2P}{5}$

$\sf :\implies\: P + \dfrac{2P}{5} = 16800$

$\sf :\implies\: \dfrac{5P + 2P}{5} = 16800$

$\sf :\implies\: \dfrac{7P}{5} = 16800$

$\sf:\implies\: 7P = 16800 \times 5$

$\sf:\implies\: 7P = 84000$

$\sf :\implies\: P = \dfrac{84000}{7}$

$\bf:\implies\: P = 12000$

Hence, the money borrowed by Mr.Sharma is ₹12000.