A man invested some amount, out of Rs.47000 he invested on simple interest at 12 p.a. for two years and rest amount on compound interest also for two years at 15% p.a. If compound interest received by is Rs.532.5 more than simple interest, then find amount invested by man on compound interest?

The correct option is Rs.21000.

Let's solve the problem step-by-step.

Step 1: Define the variables for the investments.

Let the total amount invested be Rs. 47000.

Let the amount invested in compound interest (CI) be $x$ rupees.

Then, the amount invested in simple interest (SI) will be $(47000-x)$ rupees.

Step 2: Calculate the Simple Interest (SI).

Simple Interest is calculated using the formula:

$\text{SI}=\frac{P\times R\times T}{100}$

Given for SI:

Principal ($P$) = $47000-x$

Rate ($R$) = 12% per annum

Time ($T$) = 2 years

Substituting these values into the formula:

$\text{SI}=\frac{(47000-x)\times 12\times 2}{100}$

$\text{SI}=\frac{24(47000-x)}{100}=0.24\times (47000-x)$

$\text{SI}=11280-0.24x$

Step 3: Calculate the Compound Interest (CI).

Compound Interest for 2 years at rate $R$ can be found using the net effective rate formula:

$\text{Effective Rate}=R+R+\frac{R\times R}{100}$

For $R=15\%$:

$\text{Effective Rate}=15+15+\frac{15\times 15}{100}=30+2.25=32.25\%$

So, the total Compound Interest is:

$\text{CI}=32.25\%\text{of}x=0.3225x$

Step 4: Set up the equation using the given difference between CI and SI.

According to the problem, the compound interest received is Rs. 532.5 more than the simple interest:

$\text{CI}-\text{SI}=532.5$

Substitute the expressions for CI and SI into the equation:

$0.3225x-(11280-0.24x)=532.5$

$0.3225x-11280+0.24x=532.5$

$0.5625x-11280=532.5$

$0.5625x=11280+532.5$

$0.5625x=11812.5$

Step 5: Solve for $x$.

$x=\frac{11812.5}{0.5625}$

$x=21000$

Therefore, the amount invested by the man on compound interest is Rs.21000.