Question

A given number is trebled to get a second number. This number is also trebled to get a third number. The sum of these three numbers is 12 more than 12 times the original number. Find the original number.

Answer 1

Hint: In the given question, we have been given that there is a number. This number is trebled or tripled to get a second number. Then, this second number is again tripled to get a third number. Then, the sum of the three numbers obtained after trebling is equal to 12 times the original number plus twelve. We have to find the first number by solving this system of numbers. We are going to solve this number by assuming the first number as any variable. Then we are going to form the equations by using what has been given in the question and solving for the first number. And that is going to give us our answer.

Complete step-by-step answer:
Let the original number be \[x\].
Then, it has been given that the second number is triple of the first number,
Second number \[ = 3x\]
Now, the third number is triple of second number,
Third number \[ = 3 \times 3x = 9x\]
Now, the sum of the three numbers is 12 more than 12 times the original number,
\[x + 3x + 9x = 12x + 12\]
$\Rightarrow$ \[13x = 12x + 12\]
Solving for \[x\] we have,
$\Rightarrow$ \[13x - 12x = 12\]
Hence, \[x = 12\]
Thus, the original number is \[12\].

Note: So, for solving questions of such type, we first write what has been given to us. Here we have to make one variable as x then according to the given condition write the equation and solve to get an answer.