A person lends 40% of his sum of money at 15% per annum, 50% of rest at 10% per annum and the rest at 18% per annum rate of interest. What would be the annual rate of interest, if the interest is calculated on the whole sum ?

To find the annual rate of interest on the whole sum, we need to calculate the interest earned on each portion of the sum and then add them together.

Let's assume the person's sum of money is $100.

First, the person lends 40% of $100, which is$40, at an interest rate of 15% per annum. The interest earned on this portion would be $40 * 0.15 =$6.

Next, the person lends 50% of the remaining amount, which is $60, at an interest rate of 10$60 * 0.10 = $6.

Finally, the person lends the remaining 10% of the sum, which is $10, at an interest rate of 18$10 * 0.18 = $1.80.

Now, let's add up the interest earned on each portion: $6 +$6 + $1.80 =$13.80.

To find the annual rate of interest on the whole sum, we divide the total interest earned ($13.80) by the original sum of money ($100) and multiply by 100 to get the percentage.

Therefore, the annual rate of interest on the whole sum would be ($13.80 /$100) * 100 = 13.8%.