Question

Difference between two numbers is 40.Three times the smaller number is equal to twice the bigger number Find the number.

Answer 1

Let the bigger/greater number be x and the smaller number be y.

Hence,

x - y = 40 $~~~~~~~$Equation (I)

3y = 2x $~~~~~~~$Equation (II)

From equation (II),

2x - 3y = 0

Multiplying equation (I) by 3 and equation (II) by 1,

3x - 3y = 120

2x - 3y = 0

(-)$~~~$(+)$~$= (-)$~~~~~~~$[Subtracting]

--------------------

x = 120

Substituting the value of x in equation (I),

120 - y = 40

y = 120 - 40

y = 80

Therefore,

x = 120, y = 80
The smaller number is 80 and the greater number is 120.

Answer 2

$\sf{\large {\underline {LINEAR \:EQUATIONS \:IN\:TWO\:VARIABLES}}}$ :

Let the smaller number be y and greater number be y.

Difference of these numbers = 40

x - y = 40 --> ( i )

x = 40 + y

According to the question,

3y = 2x --> ( ii )

Putting the value of " x " in equation ( ii ),

3y = 2( 40 + y )

3y = 80 + 2y

3y - 2y = 80

$\fbox {y\: =\: 80}$

Now, Putting value of " y " in equation of ' x ',

x = 40 + y

x = 40 + 80

$\fbox{x\: = \:120}$

$\sf{\underline {The \:smaller \:number \:is \:80\:and\:greater\:number \:is\:120}}$.