Question

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

Answer 1

Calculating the number of notes of each denominations

Let Number of notes of $\mathrm{Rs}100$ $=$$2\mathrm{x}$

Let Number of notes of $\mathrm{Rs}50$ $=$ $3\mathrm{x}$

Let Number of notes of $\mathrm{Rs}10$$=$ $5\mathrm{x}$

So, the value of all the denominations will be as follows

$\Rightarrow$Value of notes of$\mathrm{Rs}100$ is $=$ $\left(2\times 100\right)\mathrm{x}$ $=$$200\mathrm{x}$

$\Rightarrow$Value of notes of $\mathrm{Rs}50$ is $=$ $\left(3\times 50\right)\mathrm{x}$$=$$150\mathrm{x}$

$\Rightarrow$Value of notes of $\mathrm{Rs}10$ is$=$ $\left(5\times 10\right)\mathrm{x}$$=$$50\mathrm{x}$

Total Amount of cash in bank$=$ $\mathrm{Rs}400000$

$$\begin{gathered} 200\mathrm{x}+150\mathrm{x}+50\mathrm{x}=400000 \\ \Rightarrow 400\mathrm{x}=400000 \\ \Rightarrow \mathrm{x}=1000 \end{gathered}$$

$\Rightarrow$Number of notes of $\mathrm{Rs}100$ $=2\times 1000=2000$

$\Rightarrow$Number of notes of $\mathrm{Rs}50=3\times 1000=3000$

$\Rightarrow$Number of notes of $\mathrm{Rs}10=5\times 1000=5000$

Therefore, Lakshmi have $2000,3000$ and $5000$ notes of $\mathrm{Rs}100,\mathrm{Rs}50$ and $\mathrm{Rs}10$ respectively.