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. 4,00,000 $. How many notes of each denomination does she have?

Given:

Lakshmi 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 \( Rs. 4,00,000 \).

To do:

We have to find the notes of each denomination she has.

Solution:

Let the notes of denominations Rs. \( 100, Rs.50 \) and \(Rs. 10 \) be $2x,\ 3x$ and $5x$ respectively.

The ratio of the number of these notes is $2:3:5$ respectively.

Therefore,

$Rs.\ 100\times2x + Rs.\ 50\times3x + Rs.\ 10\times5x =Rs.\ 4,00,000$

$\Rightarrow\ 200x+150x+50x=4,00,000$

$\Rightarrow\ 200x+150x+50x=4,00,000$

$\Rightarrow\ 400x=4,00,000$

$\Rightarrow\ x=\frac{400000}{400}$       

$\Rightarrow\ x=1000$

This implies,

$2x=2\times1000=2000$

$3x=3\times1000=3000$

$5x=5\times1000=5000$

Therefore,

The notes of each denomination she has are $2000,\ 3000$ and $5000$ respectively.

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Updated on: 10-Oct-2022

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