Gappu invested Rs X at 8% simple interest for three years in a scheme and he invested the same sum for four years at 4% simple interest in another scheme. If the total interest get by Gappu from both the schemes is Rs 398, then find X.

The correct answer is 995.

Step-by-Step Explanation:

Let the sum of money invested in each scheme be Rs $X$.

The formula for simple interest (SI) is given by:
$\mathrm{SI}=\frac{P\times R\times T}{100}$
where $P$ is the principal, $R$ is the rate of interest per annum, and $T$ is the time period in years.

1. Interest from the first scheme:
Principal ($P$) = Rs $X$
Rate of interest ($R_1$) = 8%
Time period ($T_1$) = 3 years
Interest ($I_1$) = $\frac{X\times 8\times 3}{100}=\frac{24X}{100}$

2. Interest from the second scheme:
Principal ($P$) = Rs $X$
Rate of interest ($R_2$) = 4%
Time period ($T_2$) = 4 years
Interest ($I_2$) = $\frac{X\times 4\times 4}{100}=\frac{16X}{100}$

3. Total interest equation:
According to the problem, the total interest obtained from both schemes is Rs 398.
$I_1+I_2=398$

Substituting the expressions for $I_1$ and $I_2$:
$\frac{24X}{100}+\frac{16X}{100}=398$

Combining the terms on the left-hand side:
$\frac{40X}{100}=398$

Simplifying the fraction:
$\frac{2X}{5}=398$

Solving for $X$:
$X=\frac{398\times 5}{2}$
$X=199\times 5$
$X=995$

Therefore, the value of $X$ is Rs 995.