A man invests Rs. 8000 at 80% per annum simple interest for 1 year and Rs. 12000 at 10% per annum compound interest for 2 years.
Find the total interest he received (in Rs).

The correct answer is 8920 (Option 8920).

To find the total interest received by the man, we need to calculate the simple interest from the first investment and the compound interest from the second investment, and then add them together.

Step 1: Calculate Simple Interest (SI) for the first investment
Principal ($P$₁) = Rs. 8000
Rate of Simple Interest ($R$₁) = 80% per annum
Time period ($T$₁) = 1 year

The formula for Simple Interest is:

$\text{SI}=\frac{P_1\times R_1\times T_1}{100}$

Substituting the given values into the formula:

$\text{SI}=\frac{8000\times 80\times 1}{100}$

$\text{SI}=80\times 80=\text{Rs.}6400$

Step 2: Calculate Compound Interest (CI) for the second investment
Principal ($P$₂) = Rs. 12000
Rate of Compound Interest ($R$₂) = 10% per annum
Time period ($n$) = 2 years

The formula for total Amount ($A$) in compound interest is:

$A=P_2{(1+\frac{R_2}{100})}^n$

Substituting the values:

$A=12000{(1+\frac{10}{100})}^2$

$A=12000{\left(\frac{11}{10}\right)}^2$

$A=12000\times \frac{121}{100}$

$A=120\times 121=\text{Rs.}14520$

Now, calculate Compound Interest ($\text{CI}$):

$\text{CI}=A-P_2$

$\text{CI}=14520-12000=\text{Rs.}2520$

Step 3: Calculate the Total Interest

$\text{Total Interest}=\text{SI}+\text{CI}$

$\text{Total Interest}=6400+2520=\text{Rs.}8920$

Thus, the total interest received is Rs. 8920.