Algebra

Linear Equation

Medium

A told B, “When I was as old as you are now, then your age was four years less than half of my present age". If the sum of the present ages of A and B is 61 years, what is B's present age in years?

✅ Correct Option: 2

Let $A$ 's present age $= a$ years and $B$ 's present age $= b$ years

When $A$ was $b$ years old, that was $(a - b)$ years ago.

At that time, $B$ 's age was $b - (a - b) = 2b - a$

According to $A$ 's statement, $B$ 's age at that time was $\dfrac{a}{2} - 4$

$2b - a = \dfrac{a}{2} - 4$

$4b - 2a = a - 8$

$4b = 3a - 8$ ... (1)

Sum of present ages is $61$ :

$a + b = 61$

$a = 61 - b$ ... (2)

Substituting (2) into (1):

$4b = 3(61 - b) - 8$

$4b = 183 - 3b - 8$

$7b = 175$

$b = 25$

Therefore $a = 61 - 25 = 36$

$B$ 's present age is $25$ years.

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A told B, “When I was as old as you are now, then your age was four years less than half of my present age". If the sum of the present ages of A and B is 61 years, what is B's present age in years?

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