If the interest is payable quarterly, after what time will Rs.$1600$ amount to Rs. $1852.20$ at $20\%$ per annum.

The correct option is C $9$ months
Amount $=Rs.1852.20$
Principal $=Rs.1600$
Rate $=20\%$ p.a. $=5\%$ per quarter
$A=P{(1+\frac{R}{100})}^T$
$1852.2=1600{(1+\frac{5}{100})}^T$
${\left(\frac{21}{20}\right)}^3={\left(\frac{21}{20}\right)}^T$
$T=3$ quarters
$T=9$ months