Question

on what sum of money will the difference between the compound interest and the simple instrest be 25 if rate of the both is 5% pa and the time is 2 years. ​

Answer 1

Let the sum of Money be p

And Time = 2 yrs

Rate of Interest = 5%

:. Difference of Simple Interest and Compound Interest = ₹25

Simple Interest =

$si = \frac{p \times r \times t}{100} \\ \\ \\ = \frac{p \times 5 \times 2}{100} = \frac{10p}{100} = \frac{p}{10}$

Compound Interest =

$ci = p( 1 + \frac{r}{100} )^{2} - p \\ \\ = p(1 + \frac{5}{100} )^{2} - p \\ \\ = p(1 + \frac{1}{20} )^{2} - p \\ \\ = p( { \frac{21}{20} }^{2} ) - p$

Difference = CI - SI

$(p( \frac{21}{20})^{2} - p) -( \frac{p}{10} ) = 25 \\ \\p (( \frac{21}{20})^{2} - 1 - \frac{1}{10} ) = 25 \: \: \: (p \: is \: taken \: common \: ) \\ \\ p( \frac{441}{400} ) - 1 - \frac{1}{10} ) = 25 \\ \\p ( \frac{441 - 400 - 40}{400} ) = 25 \\ \\ p ( \frac{1}{400} ) = 25 \\ \\ \frac{p}{400} = 25 \\ \\ p = 25 \times 400 \\ p = 10000$

Sum of Money/ Principal = ₹ 10000

Hope Helps You ✌️

Please mark as the Brainliest ‼️