Question

On the sum of money, the difference between the interest of the first year and interest of third year is rupees 210 rate than 10% per annum compounded annually find the sum invested.​

Answer 1

Answer :-

The sum of money invested is Rs. 10,000.

Step-by-step explanation

To Find :-

• The sum of money invested.

★ Solution :-

Given that,

• The difference between the interest of the first year and interest of third year is Rs. 210 rate being 10% per annum.

ㅤㅤㅤㅤㅤ Assumption

Let us assume the principal or the sum as Rs.100

Therefore,

Compound interest of 1st year = $\sf{\dfrac{100 \times 10 \times 1}{100}}$

$\sf{\longrightarrow \: \dfrac{1 \cancel{00} \times 10 \times 1}{1 \cancel{00}}}$

$\sf{\longrightarrow \: \dfrac{1 \times 10 \times 1}{1}}$

$\sf{\longrightarrow \: Rs. 10}$

∴ Amount is = Rs. 100 + Rs. 10 = Rs. 110

Compound interest of 2nd year = $\sf{\dfrac{110 \times 10 \times 1}{100}}$

$\sf{\longrightarrow \: \dfrac{11\cancel{0} \times 1 \cancel{0} \times 1}{1 \cancel{0} \cancel{0}}}$

$\sf{\longrightarrow \: \dfrac{11 \times 1 \times 1}{1}}$

$\sf{\longrightarrow \: Rs. 11}$

∴ Amount = Rs. 110 + Rs. 11 = Rs. 121

Compound interest of 3rd year = $\sf{\dfrac{121 \times 10 \times 1}{100}}$

$\sf{\longrightarrow \dfrac{121 \times 1 \cancel{0} \times 1}{10 \cancel{0}}}$

$\sf{\longrightarrow \dfrac{121 \times 1 \times 1}{10}}$

$\sf{\longrightarrow \dfrac{121}{10}}$

$\sf{\longrightarrow \cancel{\dfrac{121}{10}}}$

$\sf{\longrightarrow Rs. 12.10}$

Now, The difference between Compound Interest of 1st year and 3rd year is :-

$\sf{\longrightarrow Rs. 12.10 - Rs. 100}$

$\sf{\longrightarrow Rs. 2.10}$

According the question,

Let's find out, by applying Unitary method :-

We got,

The difference of interest in compound interest is Rs. 2.10, sum = Rs. 100

Therefore,

The difference of interest in compound interest is Rs. 210, The sum will be :-

$\sf{\longrightarrow \dfrac{100}{2.10} \times 210}$

$\sf{\longrightarrow \dfrac{21000}{2.10}}$

$\sf{\longrightarrow Rs. 10,000}$

Hence, The sum invested is Rs. 10,000.