SSC CHSL 8 Jan 2017 Shift 1 Paper

Let the given sum = Rs. $100\mathit{x}$
Rate of interest = 12% and time period = 2 years
Compound interest = $\mathit{P}[\left({1+\frac{\mathit{R}}{100})}^{\mathit{T}}-1\right]$
= $100\mathit{x}\left[{\left(1+\frac{12}{100}\right)}^2-1\right]$
= $100\mathit{x}\left[{\left(\frac{28}{25}\right)}^2-1\right]$ $=100\mathit{x}\left(\frac{784-625}{625}\right)$
= $100\mathit{x}\times \frac{159}{625}=\frac{636\mathit{x}}{25}$
Simple interest = $\frac{\mathit{P}\times \mathit{R}\times \mathit{T}}{100}$
= $\frac{100\mathit{x}\times 12\times 2}{100}=24\mathit{x}$
⇒ Difference between simple and compound interests = $\frac{636\mathit{x}}{25}-24\mathit{x}=900$
⇒ $\frac{636\mathit{x}-600\mathit{x}}{25}=900$
⇒ $36\mathit{x}=900\times 25$
⇒ $\mathit{x}=\frac{900\times 25}{36}$ $=25\times 25=625$
∴ Value of given sum = 100 × 625 = Rs.62,500