UP Police Constable Exam Model Paper 5

Given:
Principal $=$ Rs. 25000
Compound interest $=$ Rs. 8275
Rate $=10\%$
Formula used:
$\mathit{C}\mathit{I}=\mathit{P}\times [\left\{1+{\left(\mathit{R}/100\right)}^{\mathit{T}}-1\right]$
Where, $\mathit{C}\mathit{I}=$ Compound Interest, $\mathit{P}=$ Principal, $\mathit{T}=\mathrm{Time},\mathit{R}=$ Rate
Calculation:
According to the question
$\mathit{C}\mathit{I}=\mathit{P}\times [\left\{1+{\left(\mathit{R}/100\right)}^{\mathit{I}}-1\right]$
$\Rightarrow 8275=25000\times \left[{\left\{1+\left(10/100\right)\right\}}^{\mathit{T}}-1\right]$
$\Rightarrow \left(8275/25000\right)=\left[{\left\{1+\left(1/10\right)\right\}}^{\mathit{I}}-1\right]$
$\Rightarrow \left(331/1000\right)=\left[{\left(11/10\right)}^{\mathit{I}}-1\right]$
$\Rightarrow 1331/1000={\left(11/10\right)}^{\mathit{T}}$
$\Rightarrow {\left(11/10\right)}^3={\left(11/10\right)}^{\mathit{I}}$
On comparing powers both side, we get $\Rightarrow \mathit{T}=3$ years
$\therefore$ The time taken is 3 years.