Question

Lakshmi is a cashier in a bank. She has currency notes of denominations Rs. 100, Rs. 50 and Rs. 10 respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is Rs. 400000. How many notes of each denomination does she have?

Answer 1

Hint: Here, we will consider the number of notes of each denomination as 2k, 3k and 5k respectively. Since, the total money that she has is given which is Rs. 400000. We can use this given and try to form an equation in k and then we can solve it to get the value of k.

Complete Step-by-Step solution:
A ratio indicates how many times one number contains another. The numbers in a ratio may be quantities of any kind, such as counts of objects or measurements of length, weight, time etc. A ratio may be specified either by giving both constituting numbers, written as “ a to b ” or “ a:b ” or by giving just the value of their quotient $\dfrac{a}{b}$ .
Here, we have been given that the ratio of the numbers of these notes is 2:3:5.
So, let the total number of notes of Rs. 100 be = 2k
 The total number of notes of Rs. 50 be = 3k
The total number of notes of Rs. 10 be = 5k
Therefore, the total money is equal to the sum of the money that each of the denominations contributes. So, according to this total money will be = $\left( 100\times 2k+50\times 3k+10\times 5k \right)$
Since, it is already given that the total amount or the total cash with Lakshmi is = Rs 400000.
So, we have the following equation on equating these two values:
$\begin{align}
  & \left( 100\times 2k+50\times 3k+10\times 5k \right)=400000 \\
 & \Rightarrow 200k+150k+50k=400000 \\
 & \Rightarrow 400k=400000 \\
 & \Rightarrow k=\dfrac{400000}{400} \\
 & \Rightarrow k=1000 \\
\end{align}$
So, the value of k is = 1000.
Hence, total number of notes of denomination 100 is = $2k=2\times 1000=2000$
Total number of notes of denomination 50 is = $3k=3\times 1000=3000$
Total number of notes of denomination 10 is = $5k=5\times 1000=5000$

Note: Students should note here that knowing the concept of ratio is very important. Students should know that if the ratio is 2:3:5, then we can take them as numbers of the form 2k, 3k and 5k.