Question

Tinu is younger than Pinky by three years. The product of their ages is 180. Find the age of Tinu.

Answer 1

Hint: First we will assume the age of Pinky as $x$ and then we will assume the age of Tinu to be $3$ less than the age of Pinky and then we will put both these ages into the condition given in the question that their product is $180$ and then form a quadratic equation and then get the value of the age of Pinky and then we will subtract $3$ in order to get the age of Tinu.

Complete step-by-step answer:
Let the age of Pinky be $x$ years, and as it is given in the question that Tinu is three years younger than Pinky. Therefore,
The age of Tinu is = $x-3$
Now in the question it is given that the product of both their ages is $180$ ,
So, $\left( x \right)\left( x-3 \right)=180$ , now we will multiply $x$ into the bracket and expand the equation and get:
${{x}^{2}}-3x=180$ , we will now take $180$ from right hand side to the left hand side and hence:
${{x}^{2}}-3x-180=0$ , now to solve this quadratic equation we will factorise the middle term such that their product is $180$ and then the sum is coefficient of $x$ that is $3$, therefore:
 ${{x}^{2}}-3x-180=0\Rightarrow {{x}^{2}}-15x+12x-180=0$
Now we will take the common terms out:
$\begin{align}
  & \Rightarrow {{x}^{2}}-15x+12x-180=0 \\
 & \Rightarrow x\left( x-15 \right)+12\left( x-15 \right)=0 \\
 & \Rightarrow \left( x-15 \right)\left( x+12 \right)=0 \\
 & \Rightarrow x=15,-12 \\
\end{align}$
Since age cannot be negative we will neglect the negative value of $x$ and $x=15$ ,
Therefore, the age of Pinky =$x=15$ and age of Tinu = $x-3=15-3=12$.
Hence, the age of Tinu is $12$.

Note: There are other methods as well to solve the quadratic equations although middle term splitting is the easiest and simplest but we can also use completing the square method, using the quadratic formula or by graphing.