Question

The ratio of compound interests for 3 and 2 years at the same principle and same rate of interest is 273:152 . Find the rate of interest..​

Answer 1

$r^{2}$Answer:

Step-by-step explanation:

let the principle P.

so, that two equation are

and rate of compound interest R.

for, 3 years CI = p × $( 1 + R )^{3}$ -p

or CI = p × ( 1 + R )^{3} - 1

for, 2 years CI = p × ( 1 + R )^{2} -p

or CI = p × ( 1 + R )^{2} -1

as given,

$\frac{p × ( 1 + R )^{3} - 1}{ p × ( 1 + R )^{2} -1}$  = 273 / 152

or, removing p from both sides

= $r^{3}$ + $3r^{2}$ + 3r / $r^{2}$ +2r = 273/152

= r( $r^{2}$ +3r + 3) / r ( r + 2 ) = 273 / 152

removing 'r'  from numerator and denominator

= r^{2}  +3r + 3 / r + 2 = 273 / 152

= 152r^2 + 456r + 456 = 273r + 546

= 152r^2 + 183r - 90 = 0

Answer 2

Answer:

answer is 37.5%..................