Question

a sum of money lent out at simple interest amount to rs 2200in one year and rs2800in 4years. find the sum of money and the rate of interest

Answer 1

Let principal be x Case 1: P=x  A=2200, T=1 year, I=2200-x Rate=(2200-x)100/xCase 2: P=x  A=2800  T=4 years I=2800-xRate=(2800-x)100/4x Since rate is same in both cases, we equate the two equations (2200-x)100/x=(2800-x)100/4xx=2000 therefore Rate=(2200-2000)100/2000       =10%

Answer 2

Let Sum= P lent out
After 1 year , rs 2200= P (1+r/100)........ (i)
After 4 years, rs 2800= P (1+4r/100)..... (ii)
Substract (i) from (ii)

or, 2800-2200= 3Pr/100
or, 600= 3Pr/100
or, 3Pr= 60000
or, Pr= 20000...... (A)
Substitute Pr in (i)

2200= P+200
or, P= 2000
Now
from (A)
Pr=20000
2000×r= 20000
r= 10
Hence ,sum of money and rate of interest are 2000 and 10 respectively