Question

Mahesh borrowed a certain sum for two years at simple interest from Bhim.
Mahesh lent this sum to Vishnu at the same rate for two years compound interest.
At the end of two years, Mahesh received * 410 as compound interest but paid
400 as simple interest. Find the sum and rate of interest.​

Answer 1

Step-by-step explanation:

We know that SI = PTR/100

                         P = SI * 100/r*t

                            = 400 * 100 / r * 2

                            = 20000/R  ------------------ (1)

We know that CI = P(1+r/100)^n - P

 

                            = P(1+r/100)^n - 1

                     410 = 20000/R(1+r/100)^n - 1

                     410 = 20000/R(10000 + R^2 + 2000R - 10000)/10000

                     410 = 2/R(R^2 + 200R)

                     410R = 2(R^2+200R)

                     2R^2 + 400R - 410R = 0

                     2R^2 = 10R

                        R = 5.

Substitute R in (1), we get

P = 20000/5

   = 4000.

Sum = 4000, Rate of interest 5%