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 interst.At the end of two years,MAhesh recieved rupees 410 as compound interest but paid rupees 400 as simple interest.find the sum and rate of interest

Answer 1

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%.


Hope this helps!

Answer 2

Principle= p (let)

Rate = r (let)

Time= 2 years

Si=400

Principle=si x 100/r x t

400x100/r x 2=

20000/r

Ci=p{(1+r/100)^2-1}

20000/r{(100+r/100)^2-1}

20000/r{100+r^2+200r+10000}/10000

20000/r{r^2+200r}/10000

Ata

410=20000/r{r^2+200r}/100

410xr/20000=r^2+200r/10000

410xr×10000/20000=r(r+200)

(R r cut)

205r=r+200

R=205-200

R=5

Therefore rate= 5%

And principle=20000/5=4000. Answer

I hope it helps you