Mr.Raju lent out a certain sum on S.I and the same sum on C.I at a certain rate of interest p.a. If the ratio between the difference of C.I and S.I of 2 years and 3 years is 10:31, what is the rate of interest p.a?
Question
Mr.Raju lent out a certain sum on S.I and the same sum on C.I at a certain rate of interest p.a. If the ratio between the difference of C.I and S.I of 2 years and 3 years is 10:31, what is the rate of interest p.a?
Solution
To solve this problem, we need to use the formulas for Simple Interest (SI) and Compound Interest (CI) and the given ratio.
The difference between CI and SI for 2 years is given by the formula: Pr^2/100^2, where P is the principal amount and r is the rate of interest.
The difference between CI and SI for 3 years is given by the formula: Pr^2(300+r)/100^3.
Given that the ratio of these two differences is 10:31, we can set up the following equation:
(Pr^2/100^2) / (Pr^2(300+r)/100^3) = 10/31.
Solving this equation for r, we get:
r^2 / (r^2(300+r)) = 10/31.
Simplifying, we get:
1 / (300 + r) = 10/31.
Solving for r, we get:
r = 3100/10 - 300 = 10%.
So, the rate of interest per annum is 10%.
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