A man lent a part of ₹30,000 at the rate of 10% per annum and the remaining at the rate of 8% per annum simple interest. The total interest he received after 3 years is ₹8,280. Find the amount he lent at 10% per annum.

Correct option is D

Given:

Total amount lent = ₹30,000

Rate of interest for part of the amount = 10% per annum

Rate of interest for the remaining part = 8% per annum

Total interest after 3 years = ₹8,280

We are asked to find the amount lent at 10% per annum.

Formula Used:

Simple Interest =$$\frac{P \times R \times T}{100}$$​

where:

P = principal amount

R = rate of interest

T = time period (in years)

Solution:

Let x be the amount lent at 10% per annum, then the remaining amount lent at 8% per annum will be 30,000 - x.
For the amount lent at 10%:

​$$\text{Interest}_{10\%} = \frac{x \times 10 \times 3}{100} = \frac{30x}{100} = \frac{3x}{10}$$​​

For the amount lent at 8%:

​$$\text{Interest}_{8\%} = \frac{(30,000 - x) \times 8 \times 3}{100} = \frac{24(30,000 - x)}{100} = \frac{24(30,000) - 24x}{100} = \frac{720,000 - 24x}{100}$$​​

The total interest is the sum of both interests:

​$$\frac{3x}{10} + \frac{720,000 - 24x}{100} = 8,280$$​​

6x + 720,000 = 828,000

6x = 828,000 - 720,000

6x = 108,000

x =$$\frac{108,000}{6} = 18,000$$​

The amount lent at 10% per annum is ₹18,000.

Alternate Method:

​$$\frac {360}{2\%}\times 100\%$$ = 18,000​