Question

The average age of a man and his son is $30$ years. The ratio of their ages four years ago was $10:3$ respectively. What is the difference between the present ages of the man and his son?

• A. $28$ years
• B. $16$ years
• C. $26$ years
• D. $44$ years
• E. None of these

Answer 1

The correct option is A $28$ years

Let the age of man be $x$ years and age of man be $y$ years

Average age=$30$

$\therefore$ $\frac{x+y}{2}=30$

$\therefore$ $x+y=60$........(1)

Thhe ratio of their ages four years ago was $10:3$

$\therefore$ $\frac{x-4}{y-4}=\frac{10}{3}$

On simplifying we get $3x-10y=-28$......(2)

Multiplying equation (1) by $3$

we get, $3x+3y=180$.....(3)

Subtracting equation (1) from equation (3) we get,

$-13y=-208$

$y=16$

Substituting value of $y$ in equation (1)

we get $x=44$

Therefore its difference= $44-16=28$