The C I on a certain sum for 2 years is Rs 410 and S I is Rs - Maths - Comparing Quantities

Question

The C I on a certain sum for 2 years is Rs 410 and S I is Rs 400
The rate of interest per annum is ______________

Lalit Mehra · Accepted Answer

Dear Student!

Let the sum of money be Rs P and rate of interest be r % p.a.

S.I. on the sum of money, Rs P for 2 year $= Rs \frac{P ×r × 2}{100} = R s \frac{2 p r}{100}$

$∴ \frac{2 P r}{100} = 400 (Given) ... (1)$

C.I on the given sum of money, Rs P for 2 years

$= Rs.P (1 + \frac{r}{100})^{2} - Rs.P ∴ P [(1 + \frac{r}{100})^{2} - 1] = 410 (Given) ... (2)$

Dividing (1) by (2), we get

$\frac{P [(1 + \frac{r}{100})^{2} - 1]}{\frac{2 Pr}{100}} = \frac{410}{400} ∴ \frac{(\frac{r^{2}}{10000} + \frac{2 r}{100} + 1 - 1)}{\frac{2 r}{100}} = \frac{41}{40} \Rightarrow \frac{\frac{r^{2} + 200 r}{10000}}{\frac{2 r}{100}} = \frac{41}{40} \Rightarrow \frac{r^{2} + 200 r}{200 r} = \frac{41}{40} \Rightarrow \frac{r}{200} + 1 = \frac{41}{40} \Rightarrow \frac{r}{200} = \frac{41 - 40}{40} = \frac{1}{40} \Rightarrow r = \frac{200}{40} = 5$

Thus, the rate of interest is 5% p.a.

Cheers!

The C.I. on a certain sum for 2 years is Rs.410 and S.I. is Rs.400. The rate of interest per annum is ______________.