Question

The difference of simple interest and compound interest of a principal in 3 years at the rate of 10% per annum is rupees 248 . Find the capital

Answer 1

$\tt\green{\underbrace{Answer:-(Rs.8000)}}$

$\sf\large\underline\purple{Given:}$

$\tt{\implies Compound\: interest=10\%}$

$\tt{\implies Time=3\: years}$

$\tt{\implies Difference\:_{(CI-SI)}=Rs.248}$

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

$\tt{\implies Principal=?}$

$\sf\large\underline\green{Solution:}$

• At first calculate CI and SI separately than calculate principal with the of given Interest]

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

$\tt{\implies CI=P\bigg(1+\dfrac{10}{100}\bigg)^3-P}$

$\tt{\implies CI=P\bigg(\dfrac{110}{100}\bigg)^3-P}$

$\tt{\implies CI=P\bigg(\dfrac{11}{10}\bigg)^3-P}$

$\tt{\implies CI=\dfrac{1331P}{1000}-P}$

$\tt{\implies CI=\dfrac{1331P-1000P}{1000}}$

$\tt{\implies CI=\dfrac{331P}{1000}}$

• Now, calculate SI here]

$\tt\red{\implies SI=\dfrac{P\times\:T\times\:R}{100}}$

$\tt{\implies SI=\dfrac{P\times\:3\times\:10}{100}}$

$\tt{\implies SI=\dfrac{30P}{100}}$

• Now, Calculate principal here]

$\tt\green{\implies Difference\:_{(CI-SI)}=Rs.248}$

$\tt{\implies \dfrac{331P}{1000}-\dfrac{30P}{100}=248}$

$\tt{\implies \dfrac{331P-300P}{1000}=248}$

$\tt{\implies \dfrac{31P}{1000}=248}$

$\tt{\implies 31P=248000}$

$\tt{\implies P=8000}$

$\sf\large{Hence,}$

$\tt\blue{\implies Principal=Rs.8000}$

Answer 2

$\bf\large{\underline{\underline{Question:-}}}$

The difference of simple interest and compound interest of a principal in 3 years at the rate of 10% per annum is rupees 248 . Find the capital

$\bf\large{\underline{\underline{Given:-}}}$

⊗ Rate = 10%

⊗ Difference = 248

⊗ Time = 3 years

$\bf\large{\underline{\underline{To\:Find-}}}$

⊗ Capital = ?

$\bf\large{\underline{\underline{Solution:-}}}$

Here,

we calculate C.I after that S.I

→ C.I = P=(1+r/100)ⁿ - P

→ C.I = P(1+10/100)³ - p

→ C.I= P(11/10)³ - P

→ C.I = 1331P - 1000P/1000) - P

→ C.I = 331P/1000 ----equ(1)

Now,

calculating S.I

→ S.I = P*R*T/100

→ S.I = P*10*3/100

→ S.I = 30p/100----equ(2)

★ Diffrence C.I - S.I = 248

★ By equ(1) and (2)

◆ 248 = 331p/1000 - 30p/100

◆ 248 = 331p - 300p/1000

◆ 248000 = 31p

◆ p = 248000/31

◆ p = 8000