A person invests money in three different schemes for 5 yr, 10 yr and 15 yr at 8%, 10% and 12% simple interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investment is?

Let's assume the person invests an amount of money in each scheme. Let's call these amounts A, B, and C for the 5-year, 10-year, and 15-year schemes respectively.

According to the given information, the interest earned at the completion of each scheme is the same. Let's call this interest amount I.

For the 5-year scheme, the interest earned can be calculated using the formula: I = (A * 8% * 5) / 100.

For the 10-year scheme, the interest earned can be calculated using the formula: I = (B * 10% * 10) / 100.

For the 15-year scheme, the interest earned can be calculated using the formula: I = (C * 12% * 15) / 100.

Since the interest earned is the same for all three schemes, we can equate the above equations:

(A * 8% * 5) / 100 = (B * 10% * 10) / 100 = (C * 12% * 15) / 100.

Simplifying this equation, we get:

40A = 100B = 180C.

To find the ratio of the investments, we can divide the above equation by A:

40 = (100B) / A = (180C) / A.

Dividing the first and third terms by 40, we get:

1 = (100B) / (40A) = (180C) / (40A).

Simplifying further, we get:

1 = (5B) / (2A) = (9C) / (2A).

Now, we can find the ratio of the investments:

A : B : C = 2 : 5 : 9.

Therefore, the ratio of the person's investments in the three schemes is 2 : 5 : 9.