An amount of ₹8500 becomes 9500 in 3 years time at some simple rate of interest. How much the of ₹10,200 will become in 5 years at the same rate of simple interest?

The correct option is 12200.

Let us break down the solution step-by-step.

Step 1: Find the rate of simple interest from the first scenario
In the first case, we are given:
Principal ($P$) = ₹8500
Amount ($A$) = ₹9500
Time ($T$) = 3 years

The Simple Interest ($SI$) earned is calculated as the difference between the Amount and the Principal:
$SI=A-P$
$SI=9500-8500=1000$

The formula for Simple Interest is:
$SI=\frac{P\times R\times T}{100}$
where $R$ is the rate of interest per annum.

Substitute the known values into the formula to find $R$:
$1000=\frac{8500\times R\times 3}{100}$
$1000=85\times 3\times R$
$1000=255\times R$
$R=\frac{1000}{255}=\frac{200}{51}\%$

Step 2: Calculate the simple interest for the second scenario
In the second case, we are given:
New Principal ($P_2$) = ₹10,200
Time ($T_2$) = 5 years
Rate of interest ($R$) = $\frac{200}{51}\%$ per annum

The new Simple Interest ($S{I}_2$) is:
$S{I}_2=\frac{P_2\times R\times T_2}{100}$
$S{I}_2=\frac{10200\times \frac{200}{51}\times 5}{100}$
$S{I}_2=102\times \frac{200}{51}\times 5$

Since 102 is exactly $2\times 51$:
$S{I}_2=2\times 200\times 5$
$S{I}_2=2000$

Step 3: Calculate the final Amount
The final amount ($A_2$) is the sum of the new principal and the calculated simple interest:
$A_2=P_2+S{I}_2$
$A_2=10200+2000=12200$

Therefore, the sum of ₹10,200 will become ₹12,200 in 5 years at the same rate of simple interest.