There are 2 approaches to solve this question
1. Alligation MethodEdward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, his total interest would be slightly above 2r%.
We can use allegation method which would give us approximate answer.
2r...................r
.....100/3.........
5....................4
\(\frac{6r-100}{100-3r}\)=4/5
42r=900
r=21 which is closest to 20
2. General ApproachLet principal amount = P
a. 5P/9 is invested at annual 2r% compounded semi-annually
Interest= [5P/9{1+(r/100)}^2] -5P/9
b. 4P/9 is invested at an annual rate of r% compounded annually
Interest= [4P/9{1+(r/100)}]- 4P/9
Total interest=[5P/9{1+(r/100)}^2]-5P/9 + [4P/9{1+(r/100)}]- 4P/9= P/3
Solving above equation, we will get r=20
This approach is a bit lengthy though.
kiran120680 wrote:
Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, and the remaining money at an annual rate of r% compounded annually. If after one year, Edward’s money had grown by one-thirds, the value of r is equal to which of the following?
A. 10%
B. 15%
C. 20%
D. 25%
E. 33%