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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