Question

Difference between compond and simple interest on certain sum for 2 yrs at 10% rate is 500. find the sum

Answer 1

Your Answer
$- - - - - - - - -$

T = 2 years

R = 10% p. a.

Let the sum be ₹ P.

Now,

$A = P(1 + \frac{r}{100} ) {}^{t} \\ \\ \: \: \: = P(1 + \frac{10}{100} ) {}^{2} \\ \\ \: \: \: = P \times \frac{11}{10} \times \frac{11}{10} \\ \\ \: \: \: = \frac{121p}{100}$

$CI = A - P \\ \\ \: \: \: \: \: = \frac{121p}{100} - p \\ \\ \: \: \: \: \: = \frac{121p - 100p}{100} \\ \\ \: \: \: \: \: = \frac{21p}{100}$

$SI = \frac{P \times R \times T}{100} \\ \\ \: \: \: \: \: = \frac{P \times 10 \times 2}{100} \\ \\ \: \: \: \: \: = \frac{P}{5}$

$A.T.Q \\ \\ CI - SI= 500$
$= > \frac{21p}{100} - \frac{p}{5} = 500 \\ \\ = > \frac{21p - 20p}{100} = 500 \\ \\ = > \frac{p}{100} = 500 \\ \\ = > p = 500 \times 100 \\ \\ = > p =Rs \: \: 50000$

$Hence, \: \: the \: \: sum \: \: is \: \: Rs \: \: 50000$