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:-
$${\displaystyle \frac{1}{3}}of{\displaystyle \frac{1}{2}}of{\displaystyle \frac{1}{5}}ofx=15$$
We can also write this as follows:-
$${\displaystyle \frac{1}{3}}\times {\displaystyle \frac{1}{2}}\times {\displaystyle \frac{1}{5}}\times x=15$$
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’.

$$\begin{array}{rl}& \Rightarrow {\displaystyle \frac{1}{3}}of{\displaystyle \frac{1}{2}}of{\displaystyle \frac{1}{5}}ofx=15\\ & \Rightarrow {\displaystyle \frac{1}{3}}\times {\displaystyle \frac{1}{2}}\times {\displaystyle \frac{1}{5}}\times x=15\\ & \Rightarrow x=15\times 5\times 2\times 3\\ & \Rightarrow x=450\end{array}$$
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.
$$\begin{array}{rl}& \Rightarrow {\displaystyle \frac{1}{3}}of{\displaystyle \frac{1}{2}}of{\displaystyle \frac{1}{5}}ofx=15\\ & \Rightarrow {\displaystyle \frac{1}{3}}of{\displaystyle \frac{1}{2}}of{\displaystyle \frac{1}{5}}of450=15\\ & \Rightarrow {\displaystyle \frac{1}{3}}\times {\displaystyle \frac{1}{2}}\times {\displaystyle \frac{1}{5}}\times 450=15\\ & \Rightarrow {\displaystyle \frac{1}{3}}\times {\displaystyle \frac{1}{2}}\times 90=15\\ & \Rightarrow {\displaystyle \frac{1}{3}}\times 45=15\\ & \Rightarrow 15=15\end{array}$$$$$$
As we can see that L.H.S. = R.H.S., the answer that we had calculated is correct.
Hence verified.