Siyaram invested equal sum of money in two schemes. Under scheme X, the compound interest rate was 10 p.c.p.a. and under scheme Y, the comp…

Let the principal sum = Rs. x

We know the formula for compound interest-

$( \Rightarrow {\rm{CI}} = \left[ {{\rm{P}}\left\{ {{{\left( {1 + \frac{{\rm{r}}}{{100}}} \right)}^t} - 1} \right\}} \right])$Where,

CI = Compound interest

P = Principal

R = Rate of interest

T = Time period

Under scheme X,

C.I. = 10 % p.a.

$(\begin{array}{l} \Rightarrow {\rm{CI}} = \left[ {{\rm{P}}\left\{ {{{\left( {1 + \frac{{\rm{r}}}{{100}}} \right)}^t} - 1} \right\}} \right]\\ \Rightarrow 63 = \left[ {{\rm{x}}\left\{ {{{\left( {1 + \frac{{10}}{{100}}} \right)}^2} - 1} \right\}} \right]\\ \Rightarrow 63 = \left[ {{\rm{x}}\left\{ {{{\left( {\frac{{110}}{{100}}} \right)}^2} - 1} \right\}} \right]\\ \Rightarrow 63 = \left[ {\frac{{21}}{{100}}{\rm{x}}} \right] \end{array})$

⇒ x = Rs. 300

Under scheme Y,

C.I. = 12 % p.a.

$(\begin{array}{l} \Rightarrow {\rm{CI}} = \left[ {{\rm{P}}\left\{ {{{\left( {1 + \frac{{\rm{r}}}{{100}}} \right)}^t} - 1} \right\}} \right]\\ \Rightarrow {\rm{CI}} = \left[ {300\left\{ {{{\left( {1 + \frac{{12}}{{100}}} \right)}^2} - 1} \right\}} \right]\\ \Rightarrow {\rm{CI}} = \left[ {300\left\{ {{{\left( {\frac{{112}}{{100}}} \right)}^2} - 1} \right\}} \right]\\ \Rightarrow {\rm{CI}} = \left[ {300 \times \frac{{2544}}{{10000}}} \right] \end{array})$

⇒ CI = Rs. 76.32