Question

the difrence btwn the Cl and SI on rs 8400 fr 2 yrs is rd 21 at the same r% pr yr.. find r%

Answer 1

Let rate be r% per annum.
Therefore, if principal is P and time is 2 years, rate being compounded annually;
CI=P(1+r/100)^2-P
=P(1+r^2/10000+2r/100)-P
[Using (a+b)^2 identity]
=Pr^2/10000+2Pr/100 ---(1)
And SI=Prt/100
=Pr×2/100 [For two years]
=2Pr/100 ---(2)
Therefore, Subtracting equation (2) from equation (1), we get;
CI-SI=Pr^2/10000 ----(3)
Thus,
Pr^2/10000=CI-SI
=>8400×r^2/10000=21
=>r^2=21×10000/8400
=>r^2=25
=>r=5
Hence, r% per annum = 5% per annum. [Answer]
Note: You can remember equation (3) as short method for two year problems where either principal or rate is given and the other is required.
•Short Formula (2 years):
Difference=P(r/100)^2
Hope this helps. For more clarification/discussion please comment or message.
Thanks!