Question

A motorcar is 3 times as old as its tires were when it was as old as the tires are now. When its tires are as old as the car is now, the car will be a year older than the tires are now. What are the present ages of the car and tires?

Answer 1

Answer:

Step-by-step explanation:

Let x ( in months ) denotes present age of car and y ( in months ) denotes present age of tyres.

First condition:A motorcar is 3 times as old as its tires were when it was as old as the tires are now.

Equation:

$x=3\left [ y-(x-y) \right ]\\x=3(2y-x)\\2x=3y\,\,...(i)$

Second Condition:When its tires are as old as the car is now, the car will be a year older than the tires are now.

Equation:

$x+(x-y)=y+12\\2x-y=y+12\\x-y=6\,\,...(ii)$

From equation (i), put $x=\frac{3y}{2}$ in equation (ii).

$x-y=6\\\frac{3y}{2}-y=6\\\frac{y}{2}=6\\y=12$

Put y = 12 in equation (ii).

$x=y+6=12+6=18$

So,

present age of car = 18 months

present age of tyres = 12 months