Discussion of Question with ID = 051 under Problems-on-Ages

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Question

The sum of ages of two friends is 23, whereas the product of their ages is 126. What is the sum of squares of their ages?

A

277 years.

B

278 years.

C

276 years.

D

279 years.

Soln.
Ans: a

Let the ages be x and y. We are given x + y = 23, and xy = 126. Substituting in the identity $x^2 + y^2 = (x + y)^2 - 2 × xy$, we get $x^2 + y^2 = 23^2 - 2 × 126$ = 277.

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