Find Their Ages: Solution

Pramod is 28 years old and his father is 58.

Let Pramod's age be "y" and that of his father be "x". Then, x - y = 30 and xy = 1624.

Therefore, (x-y)2 = 900. That is, x2 - 2xy + y2 = 900.

Now, x2 - 2xy + y2 = 900 can be re-written as: x2 + 2xy + y2 - 4xy = 900.

But, x2 + 2xy + y2 = (x + y)2.

Therefore, (x + y)2 - 4xy = 900.

We have xy = 1624. So, 4xy = 4 * 1624 = 6496.

Therefore, (x + y)2 - 6496 = 900.

So, (x + y)2 = 7396.

Therefore (x + y) = √ 7396.

Therefore, x + y = +86 or x + y = -86. But we are considering ages and, so, x + y cannot be negative. So, (x + y) = 86.

Now, (x + y) = 86 and (x - y) = 30. Adding the two: 2x = 116; therefore x = 58. x - y = 30; so, 58 - y = 30. Therefore, y = 28.

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