Question

6. 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

Answer:

We know that SI = PTR/100

P = SI * 100/r*t

= 400*100/r2

(1)

= 20000/R

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

Step-by-step explanation:

Let the sum borrowed by Mahesh be RS P and rate of interest be R%p.a

Simple interest (SI)=Rs 400,N=2 years

SI=100P×N×R

P=N×RSI×100=2×R400×100

P=R20000.......... (1)

Mahesh lent this sum to vishnu at the same rate for 2 years at compound interest

CI=RS 410,N=2 years

CI=P(1+100R)N−P

CI=P[(1+100R)N−1]

410=R20000[(100100+R)2−1] .......... [From (1)]

410=R20000[1000010000+R2+200R−10000]

20000410×R=10000R2+200R

20000410×R=10000R(R+200)

20000410×10000=R+200

205=R+200

R=205−200

R=5%pa

P=520000=Rs 4000

∴ The sum borrowed by Mahesh =Rs 4000

and rate of interest +5%pa

Hope it helps..