Question

Pranam ♡

When the son will be as old as his father today, the sum of their ages then will be 126. When the father was as old as his son is today, the sum of their ages then was 38. Find their present ages. ​

Answer 1

Answer:

Step-by-step explanation:

Let son 's current age is x and father 's current age is y.

Where does the(y-x) term come from? Well, 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.

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).

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

[y+(y-x)] + [(x + (y-x))] = 126

⇒ 2y - x + y = 126

∴ 3y - x = 126 ----------(1)

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

⇒ [y - (y-x)] + [x - (y-x)] = 38

⇒ x + x - y + x = 38

⇒ 3x - y = 38

∴ y = 3x - 38 -----------(2)

Now sub equ(2) into equation 1

⇒ 3(3x-38) - x = 126

⇒ 9x - 114 - x = 126

⇒ 8x = 240

∴ x = 30 

Now y = 3x - 38

⇒ y = 3(30) - 38

∴ y = 52 

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Answer 2

$\large\underline\mathfrak\blue{Answer-}$

★present age of son = 30

★present age of father = 52

$\large\underline\mathfrak\blue{Explanation-}$

Let the present age of son be x.

Present age of father be y.

Difference of their ages be ( y - x ) as it is obvious that father is elder than his son.

$\bold\pink{According\:to\:the\:question-}$

Case 1).

When the son will be as old as his father today, the sum of their ages then will be 126.

$\therefore$ [ x + ( y - x ) ] + [ y + ( y - x ) ] = 126

$\implies$ x + y - x + y + y - x = 126

$\implies$ $\cancel{x}$ + y $\cancel{-x}$ + y + y = 126

$\implies$ 3y - x = 126

$\implies$ -x = 126 - 3y⠀⠀

$\implies$ x = 3y - 126 ⠀⠀⠀⠀⠀⠀⠀⠀⠀—eq (1)

Case 2).

When the father was as old as his son is today, the sum of their ages then was 38.

$\therefore$ [ x - ( y - x ) ] + [ y - ( y - x ) ] = 38

$\implies$ x - y + x + y - y + x = 38

$\implies$ x $\cancel{-y}$ + x + $\cancel{y}$ - y + x = 38

$\implies$ 3x - y = 38 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀—eq (2)

By substitution method,

Put x = 3y - 126 in eq (2).

$\implies$ 3 ( 3y - 126 ) - y = 38

$\implies$ 9y - 378 - y = 38

$\implies$ 8y - 378 - 38 = 0

$\implies$ 8y - 416 = 0

$\implies$ 8y = 416

$\implies$ y = $\dfrac{416}{8}$

$\implies$ y = 52

$\therefore$ Present age of father is 52 years.

Now, put y = 52 in eq (2)

$\implies$ 3x - 52 = 38

$\implies$ 3x = 38 + 52

$\implies$ 3x = 90

$\implies$ x = $\dfrac{90}{3}$

$\implies$ x = 30

$\therefore$ Present age of son is 30 years.

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