Question

8. A man borrowed Rs. 200 and paid back
Rs. 250 after 2 years. The rate of interest
per annum is​

Answer 1

Answer :-

• The rate of interest is 12.5% per annum.

Given :-

• A man borrowed Rs 200 and paid back Rs 250 after 2 years.

To find :-

• The rate of interest per annum.

Step-by-step explanation :-

• Here, the principal, amount and time have been given to us. We have to find the rate of interest per annum.

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Before finding the rate of interest per annum, we have to find out the simple interest!

We know that :-

$\underline{\boxed{\sf SI = Amount - Principal}}$

Here,

• Amount = Rs 250.
• Principal = Rs 200.

Hence,

$\boxed{\bf SI = 250 - 200}$

$\overline{\boxed{\bf SI = Rs \: 50}}$

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Now as we know the simple interest, let's find the rate of interest per annum!

We know that :-

$\underline{\boxed{\sf SI = \dfrac{Principal \times Rate \times Time}{100}}}$

Here,

• Simple interest = Rs 50.
• Principal = Rs 200.
• Time = 2 years.

• Let the rate of interest be r.

Substituting the given values in this formula,

$\rm 50 = \dfrac{200 \times r \times 2}{100}$

Multiplying 200 with 2,

$\rm 50 = \dfrac{400 \times r}{100}$

Multiplying 400 with r,

$\rm 50 = \dfrac{400r}{100}$

Transposing 100 from RHS to LHS, changing it's sign,

$\rm 50 \times 100 = 400r$

Multiplying 50 with 100,

$\rm 5000 = 400r$

Transposing 400 from RHS to LHS, changing it's sign,

$\rm \dfrac{5000}{400} = r$

Dividing 5000 by 400,

$\overline{\boxed{\rm 12.5 \%= r}}$

• So, the rate of interest is 12.5% per annum.

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