Question

One-third of one fourth of a number is 12. Then the number is? Choose the correct option
A. 96
 B. 144
C. 108
D. 36

Answer 1

Hint: Use the concept that One-third of one fourth of a number a, will be \[\dfrac{1}{3}\times \dfrac{1}{4}\times a\]. We just have to form an equation with the given value of the above expression to get the number a.

Complete step-by-step answer:
In the question, we have found the number such that one-third of one fourth of a number is 12.
So let the required number is a. Now, we know that if we are required to find any fraction of the number then we simply multiple that fraction and the number together to get the result. So we mean to say that one fourth of a number a is given by \[\dfrac{1}{4}\times a\] .
Next, it is also known that if we are finding the fraction of any fraction then again, we will multiply the two fractions to get the result. So, in other words we can say that the number can be fractional too.
So when we find the one fourth of a number, we get \[\dfrac{1}{4}\times a\], and when we are finding the one-third of one fourth of a number, then we will have \[\dfrac{1}{3}\times \dfrac{1}{4}\times a\].
Now, it is given that one-third of one fourth of a number is 12, so we will get the equation that will be represented as follows:
\[\begin{align}
  & \Rightarrow \dfrac{1}{3}\times \dfrac{1}{4}\times a=12 \\
 & \Rightarrow \dfrac{1}{12}\times a=12 \\
\end{align}\]
Next we just need to simplify the above equation by cross multiplication to get the value of a , which is the required number. So, we will solve for a, as follows:
\[\begin{align}
  & \Rightarrow \dfrac{1}{12}\times a=12 \\
 & \Rightarrow a=12\times 12 \\
 & \Rightarrow a=144 \\
\end{align}\]
So, finally we get the required number which is 144. Hence, the correct answer is option B.

Note: When we are finding the certain fraction of the fraction, then we have to multiply them and not add, subtract or divide them. Also, we have to form an equation which gives the result of it at the RHS.