Question

If the difference between the simple and the compound interests on some principal amount at 20% for 3 years is Rs. 48 ,then the principal amount must be​

Answer 1

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Answer}}}}}}$

Answer 2

Answer:

The Principal is Rs. 375.

Step-by-step explanation:

Given :

Rate = 20%

Difference between CI and SI = Rs. 48

Time = 3 years

To find :

The principal

Solution :

Let the Principal be P

✯ $\textsf{\underline{\underline{Simple Interest -}}}$

• Rate = 20%
• Time = 3 years
• Principal = P

$\boxed{\sf{SI = \frac{Principal \times Rate \times Time}{100}}}$

$\sf{\longrightarrow} \: SI = \dfrac{P\times 20 \times 3}{100} \\ \\ \sf{\longrightarrow} \: SI = \dfrac{60P}{100} \\ \\ \sf{\longrightarrow} \: SI = \dfrac{30P}{50} \\ \\ \sf{\longrightarrow} \: SI = \dfrac{15P}{25}$

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Compound Interest -}}}$

• Rate = 20%
• Time = 3 years
• Principal = P

${\boxed{\sf{CI= \left[P\left( 1 + \frac{R}{100}\right)^{N}}\right]-P}}$

$\sf{\longrightarrow} \: CI= P \times \left(\dfrac{120}{100}\right)^{3} - P \\ \\ \sf{\longrightarrow} \: CI= P \times \dfrac{120}{100} \times \dfrac{120}{100} \times \dfrac{120}{100} - P\\ \\ \sf{\longrightarrow} \: CI= P \times \dfrac{12}{10} \times \dfrac{12}{10} \times \dfrac{12}{10} - P \\ \\ \sf{\longrightarrow} \: CI= P \times \dfrac{6}{5} \times \dfrac{6}{5} \times \dfrac{6}{5} - P \\ \\ \sf{\longrightarrow} \: CI= P \times \dfrac{216}{125} -P \\ \\ \sf{\longrightarrow} \: CI= \dfrac{216P}{125} -P \\ \\ \sf{\longrightarrow} \: CI= \frac{216P - 125P}{125} \\ \\ \sf{\longrightarrow} \: CI= \dfrac{91P}{125}$

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Principal - }}}$

$\sf{\longrightarrow} \: \dfrac{91P}{125} - \dfrac{15P}{25} = 48 \\ \\ \sf{\longrightarrow} \: \dfrac{91P - 75P}{125} = 48 \\ \\ \sf{\longrightarrow} \: \frac{16P}{125} = 48 \\ \\ \sf{\longrightarrow} \: 16P = 48 \times 125 \\ \\ \sf{\longrightarrow} \: 16P = 6000 \\ \\ \sf{\longrightarrow} \: P = \dfrac{6000}{16} \\ \\ \sf{\longrightarrow} \: P = 375$

Principal = Rs. 375

$\therefore$ The Principal is Rs. 375.