Question

simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on rupees 4000 for 2 years at 10% per annum the someplace on​

Answer 1

Step-by-step explanation:

Correct Question:-

The simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is?

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

• For Simple Interest

• Rate = 8%
• Time = 3 years

• For Compound Interest

• Principal = Rs. 4000
• Time = 2 years
• Rate = 10%

The Simple Interest is half of the Compound Interest.

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

• The Principal placed on Simple Interest.

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

The formula for calculating Simple interest is:-

$\boxed{ \rm \leadsto Simple \: Interest = \dfrac{PTR}{100} }$

Here:-

• P = ?

• R = rate = 8%

• T = time = 3 years

${ \rm = \dfrac{P \times 8 \times 3}{100} }$

${ \rm = \dfrac{P \times 24}{100} }$

${ \rm = 0.24P }$

$\implies \underline{ \underline{ \: \: \: \rm Simple \: Interest = 0.24P \: \: \: } }$

Now:-

The formula for finding Compound Interest is:-

$\boxed{ \rm \leadsto Compound \: Interest = P \times \bigg(1 +\frac{r}{100}\bigg)^{n} - P}$

${ \rm = P \bigg\{ \bigg(1 +\dfrac{r}{100}\bigg)^{n} - 1\bigg \}}$

Here:-

• P = Rs. 4000

• r = 10%

• n = time = 2 years

${ \rm = 4000\bigg\{ \bigg(1 +\dfrac{10}{100}\bigg)^{2} - 1\bigg \}}$

${ \rm = 4000\bigg\{ \bigg(\dfrac{100 + 10}{100}\bigg)^{2} - 1\bigg \}}$

${ \rm = 4000\bigg\{ \bigg(\dfrac{110}{100}\bigg)^{2} - 1\bigg \}}$

${ \rm = 4000\bigg\{ \bigg(\dfrac{11}{10}\bigg)^{2} - 1\bigg \}}$

${ \rm = 4000\{ ({1.1})^2 - 1 \}}$

${ \rm = 4000\{ 1.21 - 1 \}}$

${ \rm = 4000( 0.21 )}$

${ \rm = 840}$

$\implies \underline{ \underline{ \: \: \: \rm Compound \: Interest = rs.840\: \: \: } }$

Given, The Simple Interest is half of the Compound Interest.

So:-

$\implies \rm Simple\: Interest = \dfrac{Compound \: Interest}{2}$

$\implies \rm 0.24P=\dfrac{840}{2}$

$\implies \rm P= \dfrac{840}{2 \times 0.24}$

$\implies \rm P= \dfrac{840}{0.48}$

$\implies \rm P= 1750$

$\underline{\boxed{\purple{ \therefore \rm Principal \: placed\: on\: Simple \:Interest = Rs. 1750}}}$