Question

please its urgent.. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:

A. 5% B. 8%
C. 12% D. 15%

Answer 1

Amount after 8 years=Rs.12005
Amount after 5 years=Rs.9800
Since amount after 8 years is P+(I for 8 years) and Amount after 5 years is P+(I for 5) years,
Therefore
Interest after 3 years:(Rs.12005-9800)
=Rs.2205
Interest after 1 year=Rs.2205/3=Rs.735
Interest after 5 year=Rs.735*5=Rs.3675.
Principal after 5 years=A-I=Rs.9800-Rs.3675=Rs.6125
So we get the information:
Principal=Rs.6125
Time=5 years
Interest=Rs.3675
Rate=100*SI/(P*T)
=100*3675/(6125*5)
=12
Therefore, rate of interest=12%
Ans:The rate of interest is 12% (c).

Answer 2

Principal = P
Sum = P + P r t  = P ( 1 + r * 5)  = Rs  9, 800

Sum = P ( 1 + r 8 ) = Rs 12, 005

(1 + 8 r) / ( 1 + 5 r) = 12, 005 / 9, 800

9 800 ( 1 + 8 r) = 12, 005 ( 1 + 5 r)

9 800 +  8 * 9800 r =  12, 005 + 12, 005 * 5 * r

78, 400  r  - 60, 025 r  = 12, 005 - 9, 800
   18, 375  r  =  2, 205
     r = 2205/ 18375  =   441 / 3675    = 147 / 1225  = 21 / 175  = 3 / 25
     r = 0.12    or  12%