The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250. The sum of the three numbers isa)30b)50c)60d)90Correct answer is option 'C'. Can you explain this answer?

Question

Answer

To find the sum of the three numbers, we need to first determine the values of the individual numbers. We can do this by setting up a system of equations based on the given information.

Let's assume the three numbers are 3x, 4x, and 5x, where x is a constant.

Sum of Squares:
The sum of their squares is given as 1250. We can write this as an equation:
(3x)^2 + (4x)^2 + (5x)^2 = 1250
9x^2 + 16x^2 + 25x^2 = 1250
50x^2 = 1250
x^2 = 1250/50
x^2 = 25
x = √25
x = 5

Now that we have found the value of x, we can substitute it back into our assumption to find the values of the individual numbers.

The three numbers are:
3x = 3 * 5 = 15
4x = 4 * 5 = 20
5x = 5 * 5 = 25

Sum of the Three Numbers:
To find the sum of the three numbers, we add them up:
15 + 20 + 25 = 60

Therefore, the sum of the three numbers is 60.

Hence, option 'C' is the correct answer.

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