Question

A boy will be $15$ years old in $6$ years. How old is he now?

Answer 1

Hint: The current age of the boy can be found by subtracting $1$ from the age in $6$ years from now $6$ times. Instead of the repeated subtraction, we find the current age of the boy algebraically. We will subtract $6\times 1=6$ from the age in the sixth year to get the current age of the boy.

Complete step by step solution:
Let us consider the given information.
The boy will be $15$ years old in $6$ years from now.
Now, we have the point that in the sixth year from now, the age of the boy will be $15.$
We are going to find the current age of the boy algebraically.
Let us suppose that the current age of the boy is $x.$
Now, we know that the age of the boy in $6$ years from now is $15.$
We know that the age increases by $1$ each year.
We can say that if the current age is $x,$ then the age in $6$ years can be calculated as $x+6=15.$
So, the current age $x$ can be found by subtracting $6$ from $15.$
Therefore, we will get $x=15-6.$
And, since $15-6=9,$ we will get the value of $x=9.$
Thus, the current age of the boy whose age in $6$ years will be $15$ is $x=9.$
Hence, the boy is $9$ years old now.

Note: It is easy to say that the age of the boy in the fifth year is $1$ less than the sixth year from now. So, the boy will be $14$ years old in $5$ years. Likewise, the boy will be $1$ year younger in the fourth year than the fifth year. That is, the age of the boy in $4$ years from now is $14-1=13.$ Similarly, the age of the boy in the third year will be $1$ less than the age in the fourth year. So, we get the age of the boy in the third year as $13-1=12.$ The age of the boy in $2$ years will be $12-1=11.$ The boy will turn $11-1=10$ in $1$ year. This implies that the boy is $10-1=9$ years old now. Therefore, the boy is $9$ years old now.