Question

The difference between simple interest & compound interest on Principal amount for two years at a rate of 25% is Rs. 1700. what is the principal amount?​

Answer 1

Let the Principal value of the transaction be x.

~The difference between simple interest & compound interest on Principal amount for two years at a rate of 25% is ₹ 1700.

$\\ \bullet \ {\green{\underline{\boxed{\sf{ Amount = P \left( 1 + \dfrac{r}{100} \right)^n }}}}} \\ \\ \colon\implies{\sf{ x \left( 1 + \dfrac{25}{100} \right)^2 }} \\ \\ \colon\implies{\sf{ x \left( \cancel{ \dfrac{125}{100} } \right)^2 }} \\ \\ \colon\implies{\sf{ x \left( \dfrac{5}{4} \right)^2 }} \\ \\ \colon\implies{\sf{ x \times \dfrac{5}{4} \times \dfrac{5}{4} }} \\ \\ \colon\implies{\sf{ \dfrac{25x}{16} }}$

Now, We've to find the Compound Interest by subtracting Principal from Amount as:-

$\colon\implies{\sf{ \dfrac{25x}{16} - x }} \\ \\ \colon\implies{\sf{ \dfrac{25x-16x}{16} }} \\ \\ \colon\implies{\sf{ Interest_{(Compound)} = \dfrac{9x}{16} }}$

$\\ \bullet \ {\blue{\underline{\boxed{\sf{ Interest_{(Simple)} = \dfrac{PRT}{100} }}}}} \\ \\ \colon\implies{\sf{ \dfrac{x \times 2 \times 25}{100} }} \\ \\ \colon\implies{\sf{ \dfrac{ \cancel{50} x}{ \cancel{100} } }} \\ \\ \colon\implies{\sf{ \dfrac{x}{2} }}$

Now, We know that The difference between simple interest & compound interest is ₹ 1700 so:-

$\colon\implies{\sf{ \dfrac{9x}{16} - \dfrac{x}{2} = 1700 }} \\ \\ \\ \colon\implies{\sf{ \dfrac{9x-8x}{16} = 1700}} \\ \\ \\ \colon\implies{\sf{ \dfrac{x}{16} = 1700 }} \\ \\ \\ \colon\implies{\pink{\underline{\boxed{\sf{ x = 27200 }}}}}$

Hence,

${\underline{\sf{ The \ Principal \ value \ of \ the \ transaction \ is \ Rs. \ 27200 . }}}$