Question

One third of one half of one fifth of a number is 15 then the number is:-
A) 50
B) 150
C) 15
D) 450

Answer 1

HINT:- For solving this question, we will be following the following steps:-
We will assume that the number is ‘x’.
We shall form an equation which is provided below:-
\[\dfrac{1}{3}\ \ of\ \ \dfrac{1}{2}\ \ of\ \ \dfrac{1}{5}\ \ of\ \ x\ \ =\ \ 15\]
We can also write this as follows:-
\[\dfrac{1}{3}\ \ \times \ \ \dfrac{1}{2}\ \ \times \ \ \dfrac{1}{5}\ \ \times \ \ x\ \ =\ \ 15\]
Then, we will solve this question by transposition method.

Complete step-by-step answer:
Let us now solve this question.
We shall follow the same steps as provided in the hint above.
Let the number be ‘x’.

\[\begin{align}
  & \Rightarrow \dfrac{1}{3}\ \ of\ \ \dfrac{1}{2}\ \ of\ \ \dfrac{1}{5}\ \ of\ \ x\ \ =\ \ 15 \\
 & \Rightarrow \dfrac{1}{3}\ \ \times \ \ \dfrac{1}{2}\ \ \times \ \ \dfrac{1}{5}\ \ \times \ \ x\ \ =\ \ 15 \\
 & \Rightarrow x\ \ =\ \ 15\ \ \times \ \ 5\ \ \times \ \ 2\ \ \times \ \ 3 \\
 & \Rightarrow x\ \ =\ \ 450 \\
\end{align}\]
So, the value of ‘x’ is 450.
Therefore, the answer is 450.
Hence, the correct option is (d) 450.

NOTE:- Let us now verify this question.
We shall put the value of ‘x’ in the equation and then solve the equation step by step.
\[\begin{align}
  & \Rightarrow \dfrac{1}{3}\ \ of\ \ \dfrac{1}{2}\ \ of\ \ \dfrac{1}{5}\ \ of\ \ x\ \ =\ \ 15 \\
 & \Rightarrow \dfrac{1}{3}\ \ of\ \ \dfrac{1}{2}\ \ of\ \ \dfrac{1}{5}\ \ of\ \ 450\ \ =\ \ 15 \\
 & \Rightarrow \dfrac{1}{3}\ \ \times \ \ \dfrac{1}{2}\ \ \times \ \ \dfrac{1}{5}\ \ \times \ \ 450\ \ =\ \ 15 \\
 & \Rightarrow \dfrac{1}{3}\ \ \times \ \ \dfrac{1}{2}\ \ \times \ \ 90\ \ =\ \ 15 \\
 & \Rightarrow \dfrac{1}{3}\ \ \times \ \ 45\ \ =\ \ 15 \\
 & \Rightarrow 15\ \ =\ \ 15 \\
\end{align}\]\[\]
As we can see that L.H.S. = R.H.S., the answer that we had calculated is correct.
Hence verified.