Question

A sum of ₹ 400 is in the form of denominations of ₹ 10 and ₹ 20. If the total number of notes is 50, then formulate the linear equation in one variable based on the given information. ​

Answer 1

Answer:

Let the number of 5 rupee notes be x,then

The number of 10 rupee notes =90−x

Then ,according to the question

5x+10(90−x)=500

5x+900−10x=500

5x=400

x=80

There are 80 notes of Rs.5 and 10 notes of Rs.10.

Answer 2

Given:

A sum of ₹ 400 is in the form of denominations of ₹ 10 and ₹ 20 and total number of notes is 50.

Solution:

Assume that the number of notes in the denomination of ₹ 10 is $\[x\]$ and  the number of notes in the denomination of ₹ 20 is $\[y\]$,

$\[\begin{array}{l}x + y = 50\\ \Rightarrow y = 50 - x\end{array}\]$

Now formulate a linear equation using given information i.e. A sum of ₹ 400 is in the form of denominations of ₹ 10 and ₹ 20,

$\[10x + 20y = 400\]$

Put, $\[y = 50 - x\]$

Therefore,

$\[10x + 20\left( {50 - x} \right) = 400\]$

$\[ \Rightarrow x + 2\left( {50 - x} \right) = 40\]$

Hence, the linear equation in one variable is $\[x + 2\left( {50 - x} \right) = 40\]$.