Question

c.i. and s.i. for a certain sum at certain rate of interest for 2 years are rs. 220 and rs. 200. find the principal amount.

Answer 1

please find the attachment

Answer 2

Answer:

500

Step-by-step explanation:

In the question,

Compound Interest, CI = 220 Rs.

Simple Interest, SI = 200 Rs.

Time period, t = 2 years

Now,

Let us say the Principal Amount is = P

So,

According to the Formula of Compound Interest, CI, we can say that,

$CI=P\left(1+\frac{r}{100}\right)^{n}-P\\220=P\left(1+\frac{r}{100}\right)^{2}-P\ .............(1)$

Also,

From the formula of Simple Interest, SI, we can say that,

$SI=\frac{PRT}{100}\\200=\frac{P\times r\times 2}{100}\\Pr=10000\ ..........(2)$

Now, on solving both the eqns.(1) and (2), we get,

$220=P\left(1+\frac{r}{100}\right)^{2}-P\\220=P+\frac{2Pr}{100}+\frac{Pr^{2}}{10000}-P\\220=\frac{20000}{100}+\frac{10000.r}{10000}\\220=200+r\\r=20\%$

Therefore, we can say that,

Rate of interest is, r = 20%

So,

The Principal Amount is, P = 500 Rs.

Therefore, the Principal Amount is 500 Rs.