A man invests money in three different schemes for 6 years, 10 years and 12 years, at 10%, 12% and 15% simple interest, respectively. If at the completion of each scheme, he gets the same interest then the ratio of the respective investments is:

Correct option is C

Given:

Rate of interest for money invested for 6 years, 10 years and 12years = 10%,12% and 15%

Formula Used:

​$$SI= \frac{P \times R \times t}{100}$$​​

Solution:

Let the ratio of different schemes be x:y:z

Then:

​$$\frac{x \times 10 \times 6}{100}=\frac{y \times 12 \times 10}{100}=\frac{z \times 15 \times 12}{100}$$​​

60x = 120y = 180y

x = 2y = 3z

Let x = 2y = 3z = k; then:

​$$x=k$$​​

​$$y= \frac{k}{2}$$​​

​$$z=\frac{k}{3}$$​​

​$$x:y:z = k:\frac{k}{2}:\frac{k}{3} = 1:\frac{1}{2}:\frac{1}{3}$$​​

LCM of 2 and 3 is 6

$$1\times 6:\frac{1}{2}\times 6:\frac{1}{3}\times 6 = 6:3:2$$​