Question

five years ago a man was 7 times as old as his son. after 5 yrs he will be thrice as old as his son. Find their present ages​

Answer 1

SOLUTION :-

Let,

Present age of son = x

Present age of man = y

5 years ago,

Age of son = x - 5

Age of man = y - 5

After 5 years ago,

Age of son = x + 5

Age of man = y + 5

According to the first condition,

$\longmapsto \sf y - 5 = 7( x - 5 ) \\\\\longmapsto y-5 = 7x-35\\\\\longmapsto7x - y = 30 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .....................(1)$

According to the first condition,

$\longmapsto \sf y+5= 3(x+5)\\\\\longmapsto y+5 = 3x+15 \\\\\longmapsto 3x-y = -10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .....................(2)$

Equation (1) - Equation (2),

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

Substitute the value of x in equation (1),

$\longmapsto \sf 7\times 10 - y = 30\\\\\longmapsto 70 - y = 30 \\\\\longmapsto -y = - 40 \\\\\longmapsto \bf y = 40$

Present age of man = 40 years

Present age of son = 10 years