Paul invests money in three different schemes for 2 years, 4 years and 6 years at 8%, 10% and 12% simple interest respectively. After completion of each scheme he gets same interest. Find the ratio of his investments.30:18:1045:9:510:18:4545:18:10

The problem is asking for the ratio of Paul's investments in three different schemes. The schemes have different interest rates and different time periods, but they all yield the same amount of interest.

The formula for simple interest is I = PRT, where I is the interest, P is the principal (the initial amount of money), R is the rate of interest, and T is the time.

Since the interest is the same for all three schemes, we can set up the following equations:

P1 * R1 * T1 = P2 * R2 * T2 = P3 * R3 * T3

We know the rates and times for each scheme, so we can substitute those values into the equations:

P1 * 8% * 2 years = P2 * 10% * 4 years = P3 * 12% * 6 years

Solving for P1, P2, and P3 gives us the ratios of the investments.

P1 : P2 : P3 = 1/(8% * 2 years) : 1/(10% * 4 years) : 1/(12% * 6 years)

This simplifies to:

P1 : P2 : P3 = 1/0.16 : 1/0.4 : 1/0.72

To make the ratios easier to understand, we can multiply each by 100:

P1 : P2 : P3 = 625 : 250 : 138.88

Rounding to the nearest whole number gives:

P1 : P2 : P3 = 625 : 250 : 139

So, the ratio of Paul's investments in the three schemes is approximately 625:250:139.