SSC CHSL 9 Jan 2017 Shift 1 Paper

Let the given sum = Rs. 100x
Rate of interest = 16% and time period = 2 years
Compound interest = $\mathit{P}\left[{\left(1+\frac{\mathit{R}}{100}\right)}^{\mathit{T}}-1\right]$
=$100\mathit{x}\left[{\left(1+\frac{60}{110}\right)}^2-1\right]$
= $100\mathit{x}\left[{\left(\frac{29}{25}\right)}^2-1\right]$
= $100\mathit{x}\left(\frac{841-625}{625}\right)$
= $100\mathit{x}\times \frac{216}{625}=\frac{864\mathit{x}}{25}$
Simple interest = $\frac{\mathit{P}\times \mathit{R}\times \mathit{T}}{100}$
= $\frac{100\mathit{x}\times 16\times 2}{100}=32\mathit{x}$
⇒ Difference between simple and compound interests = $\frac{864\mathit{x}}{25}-32\mathit{x}=320$
⇒ $\frac{864\mathit{x}-800\mathit{x}}{25}=320$
⇒ $64\mathit{x}=320\times 25$
⇒ $\mathit{x}=\frac{320\times 25}{64}$ $=5\times 25=125$
∴ Value of given sum = 100 × 125 = Rs.12, 500