Question

if the ratio of campound interest and simple interest difference, 2 years and 3 years is 23:7. find the raye of interest​

Answer 1

$\bold \red{hola \: friend}$

here is ur answer:-

T is the time,

Then, compound interest for 3 years = P(1 + r/100)³ - P

simple interest for 3 years = P × r × 3/100

then, CI - SI = P(1 + r/100)³ - P - 3Pr/100

= P[1 + r³/100³ + 3r²/100² + 3r/100 - 1 - 3r/100]

= P[ r³/100³ + 3r²/100² ]

= P(r/100)²[r/100 + 3]

again,

Compound interest for 2 years = P[ (1 + r/100)² - 1]

simple interest for 2 years = P × r × 2/100

C.I - S.I = P[1 + r²/100² + 2r/100 - 1 - 2r/100]

= P(r/100)²

Now, A/C to question,

{(CI-SI) for 3 years }/{(CI - SI) for 2 years} = 23/7

P(r/100)² [r/100 + 3]/P(r/100)² = 23/7

⇒r/100 + 3 = 23/7

⇒ r/100 = 23/7 - 3 = 2/7

r = 200/7 %

Hence, answer is 200/7 %