SSC CHSL 7 Jan 2017 Shift 1 Paper

Let the rate of interest = $\mathit{r}$ %
Let sum invested under simple interest = Rs. $100\mathit{x}$ and time period = 5 years
⇒ Interest earned $=\frac{75}{100}\times 100\mathit{x}=\mathit{R}\mathit{s}.75\mathit{x}$
Simple interest =$\frac{\mathit{P}\times \mathit{R}\times \mathit{T}}{100}$
⇒ $\frac{100\mathit{x}\times \mathit{r}\times 5}{100}=75\mathit{x}$
⇒ $\mathit{r}=\frac{75}{5}=15\%$
Sum invested under compound interest = Rs. 40,000 and time period = 2 years
⇒ Compound interest = $\mathit{P}\left[{\left(1+\frac{\mathit{R}}{100}\right)}^{\mathit{T}}-1\right]$
$=40,000\left[{\left(1+\frac{15}{100}\right)}^2-1\right]$
$=40,000\left[{\left(\frac{23}{20}\right)}^2-1\right]$= $40,000\left(\frac{529-400}{400}\right)$
$=100\times 129=\mathit{R}\mathit{s}.12,900$