Five years from now, the ratio of the ages of A, B and C will be 3 : 5 : 2. The sum of the squares of their present ages is 525. What is the present age of B?

Five years from now, the ratio of the ages of A, B and C will be 3 : 5 : 2.

Let's assume five years from now the ages of A, B and C will be 3y, 5y and 2y.

Present age of A = (3y-5)

Present age of B = (5y-5)

Present age of C = (2y-5)

The sum of the squares of their present ages is 525.

$$\left(3y-5\right)^2+\left(5y-5\right)^2+\left(2y-5\right)^2\ =\ 525$$

$$9y^2-30y+25+25y^2-50y+25+4y^2-20y+25\ =\ 525$$

$$38y^2-100y+75\ =\ 525$$
$$38y^2-100y+75-525\ =0$$
$$38y^2-100y-450\ =0$$
$$19y^2-50y-225\ =0$$
$$19y^2-(95-45)y-225\ =0$$
$$19y^2-95y+45y-225\ =0$$
$$19y(y-5)+45(y-5) = 0$$
(y-5) (19y+45) = 0

y = $$-\frac{45}{19}$$ or 5

As we know that ages cannot be negative. So y = 5

Present age of B = (5y-5)

= $$(5\times5-5)$$

= (25-5)

= 20 years