Question

Sameer changed Rs. 200 into Rs. 5, Rs. 20 and Rs. 50 notes. If the number of Rs. 5 notes was double the number of Rs. 20 notes, and the Rs. 50 notes were one-fifth of the Rs. 20 notes, how many notes of each denomination did he get?

Answer 1

Hint: First let us assume that number of Rs. 20 notes be $ x $ . Then as given in the question that a number of Rs. 5 notes was double the number of Rs. 20 notes, and the Rs. 50 notes were one-fifth of the Rs. 20 notes we form equations. Then we will calculate the amount of each denomination and equate the sum to 200 and solve further to get the desired answer.

Complete step by step answer:
We have been given that Sameer changed Rs. 200 into Rs. 5, Rs. 20 and Rs. 50 notes.
We have to find the number of notes for each denomination he gets.
Let us assume that Sameer has a $ x $ number of Rs. 20 notes.
As given in the question the number of RS. 5 notes was double the number of Rs. 20 notes.
So, the number of Rs. 5 notes will be $ =2x $
Also, we have given in the question that the Rs. 50 notes were one-fifth of the Rs. 20 notes.
So, the number of Rs. 50 notes will be $ =\dfrac{1}{5}x $
Now, the amount of Rs. 5 notes will be $ =2x\times 5=10x $
Now, the amount of Rs. 20 notes will be $ =x\times 20=20x $
Now, the amount of Rs. 50 notes will be $ =\dfrac{1}{5}x\times 50=10x $
Now, Sameer has total of Rs. 200 so we get
 $ \begin{align}
  & \Rightarrow 10x+20x+10x=200 \\
 & \Rightarrow 40x=200 \\
 & \Rightarrow x=\dfrac{200}{40} \\
 & \Rightarrow x=5 \\
\end{align} $
Now, the number of Rs. 5 notes will be $ =2x=2\times 5=10 $
Now, the number of Rs. 50 notes will be $ =\dfrac{1}{5}x=\dfrac{5}{5}=1 $
So, Sameer gets 10,5 and 1 note of each Rs. 5, Rs. 20 and Rs. 50 respectively.

Note:
 The key concept to solve this question is the assumption of one of the common terms equal to a variable. Also, it is necessary to calculate the amount of each denomination as we have given in the question the total amount. The possibility of mistake is when students directly add $ x,2x $ and $ \dfrac{x}{5} $ and equate it to the 200. It leads to an incorrect answer.