Question

the SI on a certain sum of money for 2 years is rupees 800 and the CI on the same rate for same period is rupees 840 find the rate of interest​

Answer 1

$\sf{Simple \:Interest \:=\:\frac{P\:\times\:R\:\times\:T}{100}}$

The simple interest on a certain sum of money for 2 years is Rs. 800.

=> Simple interest for 2 years = $\sf{\frac{800}{2}}$

=> Rs. $\sf{400}$

$\therefore$ Compound interest for 1 year = Simple interest for 1 year.

So,

→ Compound interest for 1 year = Rs. 400

According to question,

Compound interest for 2 years = Rs. 840

Compound interest for 2nd year = Rs. 840 - Rs. 400

= Rs. 420

Difference between compound interest = Rs. 420 - Rs. 400

= Rs. 20

Now,

$\sf{Simple \:Interest \:=\:\frac{P\:\times\:R\:\times\:T}{100}}$

=> $\sf{20 \:=\:\frac{400\:\times\:R\:\times\:1}{100}}$

=> $\sf{20\:=\:\frac{4\:\times\:R}{1}}$

=> $\sf{\frac{20}{4}\:=\:R}$

=> $\sf{R\:=\:5\%}$

•°• The rate of interest is 5%.

Answer 2

$\huge{\boxed{\boxed{\mathfrak{\red{Answer:-}}}}}$

${\bold{\underline{\underline{Given:-}}}}$

✏Simple interest on a certain sum of money for two years = Rs800

✏Simple interest for 1year = 800/2= 400

✏Compound interest of 1year = Simple interest of 1year = 400

✏Compound interest for two years = Rs840

${\bold{\underline{\underline{formula:-}}}}$

$\small\ Simple \: interest =\frac {P \times\ R \times\ T}{100}$

${\bold{\underline{\underline{Step-by-Step-explanation:-}}}}$

✴Compound interest for 2nd year = 840-400= 420

✴Difference of CI of 1st year and 2nd year ➡420-400 =20

So,

Simple interest = 20

$\small\implies\frac {P \times\ R \times\ T}{100} = 20 \\ \\ \implies\frac {400 \times\ R \times\ 1}{100} =20 \\ \\ \implies\ 4 \times\ R = 20 \\ \\ \implies\ R =\frac {20}{4} \\ \\ \implies\ R =5$

•°•Rate of interest is 5% ......♥