Question

A sum of money lent out at Compound interest increases in value by 50% in 5 years. A person wants to lend three different sum x, y and z for 10, 15 and 20 years respectively at the above rate in such a way that he gets back equal sum at the end of their respective periods. The ratio x: y : z is
A) 6 : 9 : 4
B) 9 : 4 : 6
C) 9 : 6 : 4
D) 6 : 4 : 9

Answer 1

ans is option C

option c) 9:6:4

Answer 2

(c) 9:6:4

From the given the person wants to lend three different sum x, y and z for 10,15 and 20 years respectively as the compound interest increases in value by 50% in 5 years  

To find the ratio of x,y and z the following method is used  

Let k=$(\frac{3}{2})^2x=(\frac{3}{2})^3y=(\frac{3}{2})^4z$

Then x = $(\frac{2}{3})^2 k , y = (\frac{2}{3})^3 k, z= (\frac{2}{3})^4 k$

∴ x : y : z = $(\frac{2}{3})^2k : (\frac{2}{3})^3 k : (\frac{2}{3})^4k$  

= $1:\frac{2}{3} :(\frac{2}{3})^2$  

=$1:\frac 2 3:\frac 4 9$  

9 : 6 : 4

∴ The ratio x : y : z is 9 : 6 : 4.