Question

26. If Rs 250 amounts to Rs285(simple
interest) in two years, find the rate of
interest per annum?​

Answer 1

Answer :-

• The rate of interest is 7% per annum.

Given :-

• Principal = Rs 250.
• Amount = Rs 285.
• Time = 2 years.

To find :-

• The rate of interest per annum.

Step-by-step explanation :-

• In this question, the principal, amount and time has been given to us. We have to find the rate of interest per annum, but for that we first have to find the simple interest and then we can use it to find out our answer.

Calculations :-

• Let's find the simple interest first.

We know that :-

$\underline{\boxed{\sf Simple \: Interest = Amount - Principal.}}$

Here,

• Amount = Rs 285.
• Principal = Rs 250.

Hence,

$\tt Simple \: Interest = Rs \: 285 - Rs \: 250$

$\overline{\boxed{\tt Simple \: Interest = Rs \: 35.}}$

• Now, let's find the rate of interest!

We know that :-

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

Here,

• Simple Interest = Rs 35.
• Principal = Rs 250.
• Time = 2 years.

• Let the rate be r.

Substituting these values in the given formula,

$\tt 35 = \dfrac{250 \times r \times 2}{100}$

Multiplying 250 by 2,

$\tt 35 = \dfrac{500 \times r}{100}$

Multiplying 500 by r,

$\tt 35 = \dfrac{500r}{100}$

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

$\tt 35 \times 100 = 500r$

On simplifying,

$\tt 3500 = 500r$

Transposing 500 from RHS to LHS, changing it's sign,

$\tt \dfrac{3500}{500} = r$

Dividing 3500 by 500,

$\underline{\boxed{\tt 7 = r}}$

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• Hence, the rate of interest per annum = 7%.