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?
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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