Question

Ravi works as a cashier in a bank. He has currency of denominations Rs.100, Rs.50, Rs.10 respectively. The ratio of the number of these notes is \[2:3:5\]. The total cash with Ravi is Rs.4,00,000. How many notes of cash of each denomination does he have?

Answer 1

Hint: In this problem, we are given that Ravi works as a cashier in a bank. He has currency of denominations Rs.100, Rs.50, Rs.10 respectively. The ratio of the number of these notes is \[2:3:5\]. The total cash with Ravi is Rs.4,00,000. We have to find how many notes of cash of each denomination he has. As we are given the ratio of the number of these notes is \[2:3:5\], we can assume 2x, 3x, 5x as the number of Rs.100, Rs.50, Rs.10 notes respectively. We can now add them and find the value of x, to find the value of each Rs.100, Rs.50, Rs.10 notes respectively.

Complete step by step solution:
Here, we are given that Ravi works as a cashier in a bank. He has currency of denominations Rs.100, Rs.50, Rs.10 respectively. The ratio of the number of these notes is \[2:3:5\]. The total cash with Ravi is Rs.4,00,000.
As we are given the ratio of the number of these notes is \[2:3:5\], we can assume as,
Let, the number of Rs.100 notes = 2x ……. (1)
The number of Rs.50 notes = 3x …….. (2)
The number of Rs.10 notes = 5x …….. (3)
We can now write as,
The total amount is the addition of the given data, we get
\[\Rightarrow \left( 2x\times 100 \right)+\left( 3x\times 50 \right)+\left( 5x\times 10 \right)\]
We can now simplify the above step, we get
\[\Rightarrow 200x+150x+50x=400x\]
We know that the total amount given in this problem is 4,00,000
\[\begin{align}
  & \Rightarrow 400x=400000 \\
 & \Rightarrow x=1000 \\
\end{align}\]
We can now substitute the x value in (1), (2), (3), we get
The number of Rs.100 notes,
\[\Rightarrow 2\times 1000=2000\]
The number of Rs.50 notes,
\[\Rightarrow 3\times 1000=3000\]
The number of Rs.10 notes,
\[\Rightarrow 5\times 1000=5000\]
Therefore, there will be 2000 number of Rs.100 notes, 3000 number of Rs.50 notes and 5000 number of Rs.10 notes.

Note: We should always remember that the total amount is written in such a way that the assumed number of notes is multiplied to the respective amount and then added to the remaining multiplications of notes, with its respective amount. We should equate them with the given total amount, to get the required number of notes.