Question

in the same rate of interest the difference of two principal is Rs. 200 and the difference between the interest per annum is Rs.25 . find the rate of interest?​

Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\text{Suppose,} \\ \\ \: \: \: \: \: \: \: \text{</p><p></p><p>The \: two \: principals \: are \: x \: and \: y } \\ \: \: \: \: \: \: \: \: \: \text{respectively.} \\ \\ \: \: \: \: \: \: \: \: \: \text{Time ,t = 1 year }\\ \\ \text{</p><p>And,} \\ \\ \: \: \: \: \: \: \: \: \text{</p><p>Rate of interest = r}$

$\underline{ \bold{ \: \:Given \: : \mapsto}} \\ \\ \text{</p><p></p><p>Difference \: between \: the \: principals \: is \: Rs. 200. }\\ \\ \: \: \: \: \: \: \: \: \bold{ \therefore \: \: x - y = 200 \: \: - - - - - - - - > (1)}\\ \\ \text{Difference \: between \: the \: interest \: is \: Rs. 25} \\ \\ \bold{ \therefore \: \: \frac{ \: x.r.t \: }{100} - \frac{ \: y.r.t \: }{100} = 25 }\\ \\ \bold{ \Rightarrow \: \frac{r.t}{100} (x - y) = 25 }\\ \\ \bold{ \Rightarrow \: \frac{r \times 1}{100}(x - y) = 25 }\\ \\ \bold{ \Rightarrow \: \frac{r}{100} \times 200 = 25 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [From \: (1) ]} \\ \\ \bold{ \Rightarrow \: 2 \times r = 25} \\ \\ \bold{ \Rightarrow \: r = \frac{25}{2}} \\ \\ \therefore \: \text{ \underline{ \: r = 12.5 \: }}$

$\text{Hence,} \\ \: \: \: \: \: \: \: \text{Rate \:of \: interest , r = 12.5\%} \:$