Question

Five years hence, the age of jacob will be three times that of his son. Five years ago, jacob's age was seven times that of his son. What are their present ages? ​

Answer 1

Solution :-

Let :-

Present age of son = x

Present age of Jacob = y

5 years hence :-

Age of son = x + 5

Age of Jacob = y + 5

5 years ago :-

Age of son = x - 5

Age of Jacob = y - 5

According to the first condition :-

$\longrightarrow \sf 3(x+5)= y+5 \\\\\longrightarrow 3x+15 = y + 5\\\\\longrightarrow 3x-y = -10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...............(1)$

According to the second condition :-

$\longrightarrow \sf 7(x-5 ) = y - 5 \\\\\longrightarrow 7x-35 = y - 5 \\\\\longrightarrow 7x-y = 30 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...............(2)$

Equation (2) - Equation (1) :-

$\longrightarrow \sf 4x = 40 \\\\\longrightarrow \bf x = 10$

Substitute the value of x in eq(1) :-

$\longrightarrow \sf 3\times 10 -y = -10 \\\\\longrightarrow 30-y = -10-30 \\\\\longrightarrow -y = -40 \\\\\longrightarrow \bf y = 40$

Present age of son = 10 years

Present age of Jacob = 40 years