Question

A sum of money lent out at simple interest amounts to rupees 840 in 3 years and to rupees 1200 in 8 years. Find the rate of intere

Answer 1

Please see the attachment

Answer 2

The rate of interest is 11.53%

Step-by-step explanation:

Let the principal be x and rate of interest be r

Case 1:

Amount = 840

Simple interest = Amount - Principal = 840-x

Time = 3 years

Formula:$SI= \frac{P \times T \times R}{100}$

So, $840-x= \frac{x \times 3 \times r}{100}$

$\frac{840-x}{x}= \frac{3 \times r}{100}$

$\frac{840}{x}-1= \frac{3 \times r}{100}$

$\frac{840}{x}= \frac{3 \times r}{100}+1$

$\frac{840}{ \frac{3 \times r}{100}+1}= x$

Case 2:

Amount = 1200

Simple interest = Amount - Principal =1200-x

Time = 8 years

Formula:$SI= \frac{P \times T \times R}{100}$

So, $1200-x= \frac{x \times8\times r}{100}$

$\frac{1200-x}{x}= \frac{8 \times r}{100}$

$\frac{1200}{x}-1= \frac{8 \times r}{100}$

$\frac{1200}{x}= \frac{8 \times r}{100}+1$

$\frac{1200}{ \frac{8 \times r}{100}+1}= x$

So, $\frac{840}{ \frac{3 \times r}{100}+1}=\frac{1200}{ \frac{8 \times r}{100}+1}$

$r=\frac{150}{13}=11.53\%$

Hence The the rate of interest is 11.53%

#Learn more:

A sum of money lent out at simple interest amounts to 2200 rupees in one year and to 2800 rupees in four years. Find the sum of money and the rate of interest.

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