Question

One fourth of one third of two fifth of a number is 15. What will be \[40\%\] of that number?
\[\begin{align}
  & \text{(A) 140} \\
 & \text{(B) 150} \\
 & \text{(C) 180 } \\
 & \text{(D) 200} \\
\end{align}\]

Answer 1

Hint: Let us assume a number x. Now we will find \[\dfrac{2}{5}\] of the number x. Let us assume this number as y. Now we will find \[\dfrac{1}{3}\] of the number y. Let us assume this number as z. Now we will find \[\dfrac{1}{4}\] of the number z. Now we will equal this number to 15. By this we can find the value of x, y and z. Now we will find \[40\%\] of the number x.

Complete step by step solution:
Let us assume a number x.
We know that \[\dfrac{2}{5}\] of a number x is equal to \[\dfrac{2x}{5}\].
Let us assume \[\dfrac{2x}{5}\] as y.
\[y=\dfrac{2x}{5}.....(1)\]
In the similar way, \[\dfrac{1}{3}\] of a number y is equal to \[\dfrac{y}{3}\].
Let us assume \[\dfrac{y}{3}\] as z.
\[z=\dfrac{y}{3}.....(2)\]
In the similar way, \[\dfrac{1}{4}\] of a number z is equal to \[\dfrac{z}{4}\].
From the question, it is clear that
\[\begin{align}
  & \dfrac{z}{4}=15 \\
 & \Rightarrow z=60....(3) \\
\end{align}\]
Now let us substitute equation (3) in equation (2).
\[60=\dfrac{y}{3}\]
By using cross multiplication,
\[y=180....(4)\]
Now let us substitute equation (4) in equation (1).
\[180=\dfrac{2x}{5}\]
By using cross multiplication,
\[\begin{align}
  & \Rightarrow 2x=900 \\
 & \Rightarrow x=450....(5) \\
\end{align}\]
Now we have to find \[40\%\] of the number x.
 \[\Rightarrow \dfrac{40x}{100}=\dfrac{40}{100}(450)=4 \times (45)=180\]
So, the \[40\%\] of the number x is 180.

Note: This question can be solved in an alternative way.
Let us assume a number x.
One fourth of one third of two fifth of a number x \[=\dfrac{1}{4}\left( \dfrac{1}{3}\left( \dfrac{2}{5}\left( x \right) \right) \right)=\dfrac{1}{4}\left( \dfrac{1}{3}\left( \dfrac{2x}{5} \right) \right)=\dfrac{1}{4}\left( \dfrac{2x}{15} \right)=\dfrac{2x}{60}=\dfrac{x}{30}\]
Let us assume \[\dfrac{x}{30}\] as y.
\[\Rightarrow y=\dfrac{x}{30}\]
From the question, it is clear that one fourth of one third of two fifth of a number x is equal to 15.
So, the value of y should be equal to y.
\[\Rightarrow \dfrac{x}{30}=15\]
By using cross multiplication,
\[\Rightarrow x=450\]
Now we have to find \[40\%\] of x.
\[\Rightarrow \dfrac{40}{100}x=\dfrac{40}{100}(450)=180\]
Hence, option (C) is correct.