# EX.2.2 Q14 Linear Equations in One Variable Solutions - NCERT Maths Class 8

## Question

Lakshmi is a cashier in a bank. She has currency notes of denomination $$\rm{Rs}.\,100$$, $$\rm{Rs}.\,50$$ and $$\rm{Rs}.\,10$$, respectively. The ratio of the number of these notes is $$2:3:5$$. The total cash with Lakshmi is $$\rm{Rs}.\,4,00,000$$. How many notes of each denomination does she have?

Video Solution
Linear Equations
Ex 2.2 | Question 14

## Text Solution

What is known?

(i) Cashier Lakshmi has currency notes of denominaton $$\rm{Rs}.\,100$$, $$\rm{Rs}.\,50$$, and $$\rm{Rs}.\,10$$.

(ii) Ratio of the number of notes is $$2:3:5$$.

(iii) Total cash with Lakshmi is $$\rm{Rs}.\, 4,00,000$$

What is unknown?

How many notes of each denomination.

Reasoning:

Use the ratio condition and express the number of notes of different denominations in terms of a variable. Use the second condition to form a linear equation.

Steps:

(i) Lakshmi has currency notes of denomination $$\rm{Rs}.\,100$$$$\rm{Rs}.\,50$$, $$\rm{Rs}.\,10$$.

(ii) Number of notes are in ratio $$2:3:5$$, therefore number of notes is $$2x,{\rm{ }}3x$$ and $$5x$$

 Denomination Number of notes Total $$\rm{Rs}.\,100$$ $$2x$$ $$200x$$ $$\rm{Rs}.\,50$$ $$3x$$ $$150x$$ $$\rm{Rs}.\,10$$ $$5x$$ $$50x$$

\begin{align}200x + 150x + 50x &= 400000 \\400x &= 400000 \\x &= \frac{400000}{400} \\x &= 1000 \\\end{align}

 Denomination Number of notes $$\rm{Rs}.\,100$$ $$2x = 2 \times 1000 = 2000$$ $$\rm{Rs}.\,50$$ $$3x = 3 \times 1000 = 3000$$ $$\rm{Rs}.\,10$$ $$5x = 5 \times 1000 = 5000$$
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