Question & Answer
QUESTION

The present age of a father is three years more than three times the age of the son. Three years hence, the father's age will be 10 years more than twice the age of the son. Determine their present ages.

ANSWER Verified Verified
Hint: Let the present age of son be x. So the present age of the father is 3x+3 according to the details given in the question.After 3 years father's age will be 3x+6 and son’s age will be x+3 then from given condition we get 3x+6 =10+2(x+3).Hence calculate the value of x.

Complete step-by-step answer:
Let the present age of the son be \[x\] years.
It is mentioned in the question that the present age of the father is \[3x+3\] years.
So three years later,
Age of son \[=x+3.....(1)\]
Age of father \[=3x+3+3=3x+6........(2)\]
Also it is mentioned in the question that three years later the age of the father will be ten years more than twice the age of the son. Using these information, we get equation (2) equal to 10 plus twice of equation (1) that is,
 \[\Rightarrow 3x+6=10+2(x+3)........(3)\]
Rearranging equation (3) we get,
 \[\Rightarrow 3x+6=10+2x+6.......(4)\]
Bringing similar terms together on both sides of the equation (4) we get,
 \[\Rightarrow 3x-2x=10+6-6.......(5)\]
Now after cancelling similar terms from equation (5) and then solving for x we get,
 \[\Rightarrow x=10\]
So the present age of the son is 10 years and we will get the present age of father by substituting \[x=10\] years in \[3x+3\].
The present age of father \[=3\times 10+3=33\] years.
So the answer is that the age of the son is 10 years and the present age of father is 33 years.

Note: Here we are taking the present age of son to be x because the age of father is given in terms of the age of his son and also this technique consumes less time. Grasping these types of questions in one go is difficult so we will try to read it 3 to 4 times and then proceed with the solution.