Question

Two years ago, Dilip was three times as old as his son and two years hence, twice his age will be equal to five times his son. Find their present ages.

Answer 1

Hint: Notice that we get an equality from the information of present age and age after two years. We can use this information to formulate an equation which on solving will give us Dilip and his son’s age.

Complete step by step answer:
1) Assign variables for father and son’s age. One can assign any variable.
Let Dilip’s age be x and son’s age be y.
Therefore, 2 years ago, the age of the father and son is:
Dilip’s age \[ =x\]
Son’s age \[ = y\]
Therefore, Dilip’s age \[ = 3y\]
At present, their age is;
Son’s age \[ = y + 2\]
Dilip’s age\[= x + 2\]\[ = 3y +2\] ------(1)
And, after two years, their ages will be:
Son’s age \[= y + 4\]
Dilip’s age \[= x + 4 = 3y + 4\]
2) We have that 2 years later, two times (twice) Dilip’s age will be 5 times his son after 2 years,
Therefore, we get the equation,
\[= 5 ( y + 4 ) = 3 ( y + 4 )\]
Which on solving, would give us
\[\begin{array}{l}5y + 20 = 6y + 8\\5y + 20 - 6y - 8 = 0\\ - y + 12 = 0\\\therefore y = 12\end{array}\]
Hence, the age of Dilip’s son is 12. On substituting this in the equation (1), we get,
\[3(12) + 4 = 36 + 4 = 40\]

Thus, Dilip’s age is 40 at present.

Note:
1) In questions like this, writing down the information helps clear the picture.
2) Students are prone to rushing it in the end when it comes to such problems. Make sure not to make any silly mistakes.
3) Number the equations which would be required later in the problem.
4) These kinds of problems often seem easy and in a hurry students are prone to make mistakes. Rather than treating it like a puzzle, treat it like a mathematics problem and don’t solve it in your head.