Quantitative Reasoning

Linear Equation

Medium

The present age of a father is 4 years more than double the age of his son. After 10 years, the father's age is 30 years more than his son. Then the present age of father is:

26 years

28 years

56 years

60 years

✅ Correct Option: 3

Let the son's present age be $x$ years and the father's present age be $y$ years.

The father's present age is 4 years more than double the son's age:

$y = 2x + 4$ ... (1)

After 10 years, the father's age will be $y + 10$ and the son's age will be $x + 10$ .

The father's age will be 30 years more than the son's age:

$y + 10 = (x + 10) + 30$

$y + 10 = x + 40$

$y = x + 30$ ... (2)

From equations (1) and (2):

$2x + 4 = x + 30$

$2x - x = 30 - 4$

$x = 26$

The son's present age is 26 years.

Substituting $x = 26$ in equation (1):

$y = 2(26) + 4$

$y = 52 + 4$

$y = 56$

Therefore, the present age of the father is 56 years.

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Solution