Question

. The difference between the
compound interest and the simple
interest on a certain sum at 12% per
annum for 2 yr is 90. Find the
sum.​

Answer 1

$\underline\mathfrak{Given:-}$

• The compound interest and the simple interest on a certain sum of 12% per annum for 2 year is Rs. 90

$\underline\mathfrak{To \: \: Find:-}$

• Find the sum is equal to ......?

$\underline\mathfrak{Solutions:-}$

• Let the sum be Rs 100

Then, Simple interest on Rs 100 for 2 year.

$\: \: \: \: \: \leadsto \: \: Rs. \: \: \frac{({\cancel{100}} \: \times \: {12} \: \times \: {2}}{\cancel{100}})}$

$\: \: \: \: \: \leadsto \: \: Rs. \: \: {24}$

Amount when Rs. 100 is borrowed for 2 year on compound interest.

$\: \: \: \: \: \leadsto \: \: {100} \: \times \: {({1} \: + \: \cancel{\frac{12}{100}})}^{2}$

$\: \: \: \: \: \leadsto \: \: {100} \: \times \: {({1} \: + \: \frac{3}{25})}^{2}$

$\: \: \: \: \: \leadsto \: \: {100} \: \times \: {(\frac{{25} \: + \: {3}}{25})}^{2}$

$\: \: \: \: \: \leadsto \: \: {100} \: \times \: {(\frac{28}{25})}^{2}$

$\: \: \: \: \: \leadsto \: \: \cancel{100} \: \times \: \frac{28}{\cancel{25}} \: \times \: {28}{25}$

$\: \: \: \: \: \leadsto \: \: \frac{{4} \: \times \: {28} \: \times \: {28}}{25}$

$\: \: \: \: \: \leadsto \: \: {Rs.} \: \: \frac{3136}{25}$

Compound interest for 2 year

$\: \: \: \: \: \leadsto \: \: {(\frac{3136}{25} \: - \: {100})}$

$\: \: \: \: \: \leadsto \: \: {(\frac{{3136} \: - \: {100}}{25})}$

$\: \: \: \: \: \leadsto \: \: Rs. \: \: \frac{636}{25}$

Difference between CI and SI

$\: \: \: \: \: \leadsto \: \: {(\frac{636}{25} \: - \: {24})}$

$\: \: \: \: \: \leadsto \: \: {(\frac{{636} \: - \: {600}}{25})}$

$\: \: \: \: \: \leadsto \: \: Rs. \: \: \frac{36}{25}$

The difference between CI and SI is Rs. 36/25

Then, the sum = 100

Difference between CI and SI is Rs. 1, the sum.

$\: \: \: \: \: \leadsto \: \: {({100} \: \times \: \frac{25}{36})}$

The difference between CI and SI is Rs. 90, then the sum

$\: \: \: \: \: \leadsto \: \: {({100} \: \times \: {\frac{25}{\cancel{36}}} \: \times \: \cancel{90})}$

$\: \: \: \: \: \leadsto \: \: {({25} \: \times \: {\frac{25}{\cancel{4}}} \: \times \: \cancel{10})}$

$\: \: \: \: \: \leadsto \: \: {25} \: \times \: {25} \: \times \: {10}$

$\: \: \: \: \: \leadsto \: \: {6250}$

Hence, the sum is Rs. 6250.