Question

A sum of Rs. 8400 is made up of 50,20,10 and 5rupee notes. The number of 10rupee notes is five times the number of 5rupee notes, four times the 20rupee notes and ten times the number of 50rupee notes. What is the number of Rs.10 notes?
(A) 240
(B) 400
(C) 540
(D) 200

Answer 1

Hint: To solve this question, first of all we will assume the total number of 10rupee notes to be x. Then we will make equations of the relation of the number of 10rupee notes with all the other notes. Then we will find the total money in terms of the sum of 10rupee notes and compare the amount as given in the question. The answer which we will get after solving the equation will be the total number of 10rupee notes. This will be our final answer.

Complete step by step answer:
Let us start the question by assuming the total number of 10rupee notes to be x.
Then, according to the question, the number of 10rupee notes is 10 times the number of 50rupee notes. So, we can write
\[\begin{align}
  & x=10\times (\text{number of 50rupee notes}) \\
 & \Rightarrow \text{number of 50rupee notes}=\dfrac{x}{10} \\
\end{align}\]
Hence,
Number of 50rupee notes \[=\dfrac{x}{10}\]
Similarly, the number of 10rupee notes is 4 times the number of 20rupee notes. So, we can write
\[\begin{align}
  & x=4\times (\text{number of 20rupee notes}) \\
 & \Rightarrow \text{number of 20rupee notes}=\dfrac{x}{4} \\
\end{align}\]
So,
Number of 20rupee notes \[=\dfrac{x}{4}\]
Similarly, the number of 10rupee notes is 5 times the number of 5rupee notes. So, we can write
\[\begin{align}
  & x=5\times (\text{number of 5rupee notes}) \\
 & \Rightarrow \text{number of 5rupee notes}=\dfrac{x}{5} \\
\end{align}\]
So,
Number of 5rupee notes \[=\dfrac{x}{5}\]
Now,
Amount with 10rupee notes \[=10x\]
Amount with 50rupee notes \[=50\times \dfrac{x}{10}=5x\]
Amount with 20rupee notes \[=20\times \dfrac{x}{4}=5x\]
Amount with 5rupee notes \[=5\times \dfrac{x}{5}=x\]
Total amount \[=10x+5x+5x+x\]
According to the question,
\[\begin{align}
  & 8400=10x+5x+5x+x \\
 & 8400=21x \\
 & x=400 \\
\end{align}\]

So, the correct answer is “Option B”.

Note: In this question, the equations showing the relation of the number of 10rupee notes with all the other notes has to be made very carefully. Sometimes, the relation in the number of notes can be written as amount, but it is completely wrong. So, prevent this type of error. Also, the complete mathematical calculation has to be done carefully.