Question

when the sons age became fathers present age sum of their age will be 126. when fathers age was as old as the sons age the sum of their ages was 38,then find their present ages​

Answer 1

Answer: present age of son is 30 and his father is 52 years

Step-by-step explanation:

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• When the son's age became fathers present age sum of their age will be 126

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• When fathers age was as old as the sons age the sum of their ages was 38

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$\red{\underline \bold{To \: Find:}}$

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• Their present ages.

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let son's current age is x

Let father's current age is y

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Now,where does the (y − x) term come from?

It says 'when the son will be as old as the father is today, which means that the son has to age a certain amount of years. How many years does he have to age?

The difference between his current age and his father's current age.

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For example, if the son was 10 and the father was 40, it would take the son 30 years (or y − x = 40 − 10) to reach his current age. In the meantime, the father would age the same amount (y − x = 40 − 10 = 30 years).

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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[Father's new age] + [Son's new age] = 126

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[y+(y−x)]+[(x+(y−x))]=126

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⇒2y − x + y = 126

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∴ 3y − x = 126 --------(1)

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[Father's previous age] + [Son's previous age] = 38

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[y − (y − x)] + [x − (y − x)] = 38

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⇒ x + x − y + x = 38

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⇒3x − y = 38

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∴ y = 3x − 38 -------(2)

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Now substituting equation (2) into equation(1)

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⇒3(3x − 38) − x = 126

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⇒9x − 114 − x = 126

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⇒8x = 240

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∴ x = 30

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Now y = 3x − 38

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⇒y = 3(30) − 38

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∴ y = 52

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The son is 30 years old, and the father is 52 years old.

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