The sum of ages of A and B is 47 years. The product of their ages is 550. Find their ages. Assume B to be younger to A.
Let A's age $=x$ years
Since, sum of ages of A and B is 47 years $\implies$ B's age $=\left(47-x\right)$ years
Product of ages of A and B is 550
i.e. $x \left(47-x\right)=550$
i.e. $47x - x^2 = 550$
i.e. $x^2 - 47x + 550 = 0$
i.e. $x^2 - 25x - 22x + 550 = 0$
i.e. $x\left(x-25\right)-22\left(x-25\right)=0$
i.e. $\left(x-25\right)\left(x-22\right)=0$
i.e. $x=25$ or $x=22$
Since B is younger to A,
A's age $=25$ years and B's age $=47-25=22$ years