Question

The difference between the SI
and Cl on a certain sum at 10%
p.a. for 2 years is Rs. 250. Find
the sum. *​

Answer 1

$\sf\large{Given:}$

• The rate of interest=10%
• The time on sum=2 years
• Difference CI and SI=250

$\sf\large{To\: Find:}$

• The sum=?

$\sf\large{Let:}$

• The sum be P

[Calculation for si:-]

$\sf{\implies SI=\dfrac{P*T*R}{100}}$

$\sf{\implies SI=\dfrac{P*2*10}{100}}$

$\sf\red{\implies SI=\dfrac{P}{5}}$

[Calculation for CI:-]

$\sf{\implies CI=P(1+\dfrac{r}{100})^n-P}$

$\sf{\implies CI=P(1+\dfrac{10}{100})^2-P}$

$\sf{\implies CI=P(\dfrac{11}{10})^2-P}$

$\sf{\implies CI=\dfrac{121P}{100}-P}$

$\sf{\implies CI=\dfrac{121P-100P}{100}}$

$\sf\red{\implies CI=\dfrac{21P}{100}}$

[Calculation for Difference:-]

$\sf{\implies \dfrac{21P}{100}-\dfrac{P}{5}=250}$

$\sf{\implies \dfrac{21P-20P}{100}=250}$

$\sf{\implies \dfrac{P}{100}=250}$

$\sf{\implies P=250*100}$

$\sf\red{\implies P=Rs.25000}$

Hence,

• The certain sum is Rs.25000