Question

what rate gives ₹49680as interest on a sum of ₹54000in 2years ?​

Answer 1

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Answer 2

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

Let us, assume that, the interest is calculated under Simple Interest. So,

$\underline{ \mathfrak{ \: \: Given, \: \: }} \\ \\ \: \: \: \: \: \: \: \pink{\text{Interest, S.I. = Rs. 49680}} \\ \\ \: \: \: \: \: \: \: \: \green{ \text{Principle, P = Rs. 54000}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \blue{ \text{Time, n = 2 years}} \\ \\ \underline{ \mathfrak{ \: To \: \: find : \to \: \: }} \\ \\ \: \: \: \: \: \: \: \: \red{ \text{ Rate of interest, r = ? }}$

$\underline{ \mathfrak{ \: \: We \: \: know \: \: that, \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \boxed{ \bold{ \pink{ \: \: S.I. = \frac{P \times r \times n}{100} \: \: }}}$

$\underline{ \bold{ \: \: A.T.Q., \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \tt{ \pink{49680} = \frac{ \green{540 \cancel{0} \cancel{0}} \times \red{ r} \times \blue{2}}{1 \cancel{0 }\cancel{0}} } \\ \\ \tt{ \implies \: \pink{49680} = \green{540} \times \red{ r }\times \blue{ 2 }} \\ \\ \tt{ \implies \: \pink{49680} = 1080 \times \red{r}} \\ \\ \tt{ \implies \: \red{r} = \frac{ \pink{49680}}{1080} } \\ \\ \: \: \: \: \: \: \: \: \tt{ \therefore \: \red{r} = \red{46}}$

$\sf{ \: \: \therefore \: \: Rate \: \: of \: \: interest, r = \red{46\% \: }}$

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

$\underline{ \mathfrak{ \: \: We \: \: have,\: \: }} \\ \\ \: \: \: \: \: \: \: \:\green{ \text{Principle, P = Rs. 54000}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \blue{ \text{Time, n = 2 years}} \\ \\ \red{ \text{ Rate of interest, r = 46\% }} \\ \\ \underline{ \mathfrak{ \: To \: \: find : \to \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \pink{\text{Interest, S.I. = ?}}$

$\tt{ \therefore \: \pink{S.I}. = \frac{ \green{540 \cancel{0} \cancel{0} }\times \red{ 46} \times \blue{2}}{1 \cancel{0 }\cancel{0}} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = \green{540} \times \red{ 46}\times \blue{2} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = \pink{49680} }$

$\: \: \: \: \: \therefore \: \pink{\text{Interest, S.I. =Rs. 49680}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \bold{ \: \: \: \: \: \: \: \: \: Hence \: \: verified. \: }}$