Question

please answer the questions please and explain it also! if you want brainlist so answer questions please!
​

Answer 1

${\underline{{\text{Question}}}}$

The simple interest and compound interest on a certain sum of money is Rs 400 and Rs 410 respectively for 2 yrs. find principal and rate of interest?

Step-by-step explanation:

${\underline{{\text{Given}}}}$

Simple Interest (I) = Rs 400

Compound Interest (C.I) = Rs 410

Time (t) = 2 yr

${\underline{{\text{To Find:}}}}$

Principal (P)

Rate of interest (r)

${\underline{{\text{Solution:}}}}$

Let, the principal be Rs x and the rate of interest be y % per annum.

$\text{So, Simple Interest} = \frac{Prt}{100} \\ \\ = \frac{x \times y \times 2}{100} \\ \\ = \frac{2xy}{100} .........(i)$

Again,

$\text{Compound Interest}= P \{(1+\dfrac{r}{100})^{t} - 1 \} \\ \\ = x \{(1+\dfrac{y}{100})^{2} - 1 \} \\ \\ = x (1+\dfrac{y}{100} + 1 ) (1 + \frac{y}{100} - 1) \\ \\ \text{[Using} \: \: {a}^{2} - { b}^{2} = (a + b)(a - b)] \\ \\ = x(2 + \frac{y}{100} )( \frac{y}{100} ) \\ \\ = \frac{xy}{100} (2 + \frac{y}{100} ).......(ii)$

Now, Dividing (ii) by (i) I get,

$\frac{\frac{xy}{100} (2 + \frac{y}{100} )}{ \frac{2xy}{100} } = \frac{410}{400} \\ \\ \frac{ \cancel\frac{xy}{100} (2 + \frac{y}{100} )}{ \cancel\frac{2xy}{100} } = \frac{41 \cancel0}{40 \cancel0} \\ \\ \frac{(2 + \frac{y}{100} )}{2} = \frac{41}{40} \\ \\ 2 + \frac{y}{100} = 2 \times \frac{41}{40} \\ \\ \frac{y}{100} = \frac{82}{40} - 2 \\ \\ \frac{y}{100} = \frac{2}{40} \\ \\ \frac{y}{ \cancel{100}} = \frac{1}{ \cancel{20}} \\ \\ y = 5\%$

Hence, the required rate of interest is 5% .

So,

$\frac{2xy}{100} = 400 \\ \\ \frac{ 2 \times 5 \times x}{100} = 400 \\ \\ \frac{10x}{100} = 400 \\ \\ x = 4000 \times 10 \\ \\ x = 4000$

Hence, the required Principal is Rs 4000.

${\underline{{\text{ Some Important Formula Of Interest }}}}$

$i)I = \dfrac{ P rt}{100}$

Where, I = Simple Interest

P = Principal

t = time

r = rate of interest

$ii)C.I = P \{(1+\dfrac{r}{100})^{t} - 1 \}$

Where, C.I = Compound Interest