Question

Ramesh borrowed from Suresh certain sum for 2 years at simple interest.
He lent this sum to Dinesh at the same rate for 2 years compound interest.
At the end of 2 years Ramesh received 110 as compound interest from Dinesh but
paid 100 as simple interest to Suresh. Find the sum and the rate of interest.
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Answer 1

Answer:

Sum = Rs 250  & Rate of interest = 20%

Step-by-step explanation:

Let say sum = P

Rate of interest = R

Time = 2 Years

Simple interest = P * R  * 2/100   = 100

=> PR = 5000

=> P = 5000/R

Compound interest = P * (1 + R/100)²  - P  = 110

=> P (  (1 + R/100)² - 1) = 110

=> (5000/R)  (  1 + R²/10000 + 2R/100 - 1) = 110

=> 500 ( R²/10000 + 2R/100) = 11 R

=>  R²/20  + 10R = 11R

=>  R²/20 = R

=> R = 20

P = 5000/R

=> P = 5000/20 = 250

Sum = Rs 250

Rate of interest = 20%