Question

the CI on a certain sum for 2 years is rupees 41 and SI rupees 40. then the rate percent per annum is​

Answer 1

Answer:

Step-by-step explanation:

SI for 2 years=40

THUS,SI for 1 year=40/2=20

As for the first year CI and SI are always same so,

CI for first year=20

give that CI for 2 years is 41;

So CI for second year =41-20=21

Difference in CI for two successive years=21-20=1

so;

1 is the interest for one year on the interest of first year,that is,on rupees 20;

thus,

rate=(100*I)/(P*T)

=(100*1)/(20*1)

=5 percent

therefore; the rate is 5% per annum.

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Answer 2

Answer:

Required rate of interest is 5%.

Step by step explanation:

Let principle be x and rate of interest be r.

Given time t is 2 years.

For CI,

C.I=Amount-p=$p {(1 - \frac{r}{100} )}^{t}$

$41 - p = p {(1 - \frac{r}{100} )}^{2} ......(1)$

For S.I,

S.I=$\frac{prt}{100}$

$40 = \frac{2pr}{100}$

$p = \frac{2000}{r} .....(2)$

From equation (1) and (2),

$41 - \frac{2000}{r} = \frac{2000}{r} {(1 - \frac{r}{100}) }^{2}$

By solving this equation, we get r=5

So rate of interest is 5%.

Here applied formulas are

$s.i = \frac{prt}{100}$

$c.i = p {(1 - \frac{r}{100} )}^{t} - p$

${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$