Question

A two digit number when increase by 75% then its

digits gets interchanged. If difference between both

digits is 3 then find the original number?​

Answer 1

Question : A two digit number when increase by 75% then its digits gets interchanged. If difference between both digits is 3 then find the original number?

To find : 2 digit number

Let :

• two digit number = ( 10x + y )

Given :

• y - x = 3 { considering y > x } ..........1
• when increased by 75% digits get interchanged , i.e., (10y+x)

Solution :

original number is (10x+y)

according to question ,

(10x+y) + 75% of (10x+y) = ( 10y+3)

$= > \: (10x + y) \: + \: \frac{75}{100} (10x + y) = (10y + x) \\ \\ = > (10 + y)(1 + \frac{75}{100} ) = (10y + x) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = > (10x + y)(1 + \frac{3}{4} ) \: = \: (10y + x) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = > (10x + y)( \frac{7}{4} ) = (10y + x) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

{ taking LCM }

$= > (10x + y)(7) \: = \: 4(10y + x)$

=> 70x + 7y = 40y + 4x

=> 70x - 4x = 40y - 7y

=> 66x = 33y

=> x = (33/66)y

=> x = (1/2)y

putting value of x in equation 1

$= > y \: - \: \frac{1}{2} y \: = \: 3 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = > y( 1 - \frac{1}{2} ) \: = \: 3 \\ \\taking \: lcm \\ = > \: y( \frac{(1 \times 2) - (1 \times 1)}{2} ) = 3 \\ \\ = > y( \frac{(2 - 1)}{2} ) = 3 \\ \\ = > y( \frac{1}{2} ) = 3 \\ \\ \\ = > y = 3 \times ( \frac{2}{1} ) \\ \\ = > y \: = \: 6$

therefore

$x \: = \: \frac{1}{2} y \\ \\ x \: = \: \frac{1}{2} \times 6 \\ \\ x \: = \: 3 \: \: \: \:$

therefore number =>

(10x + y) = { (10×3) + 6 }

=> (30+6)

=> 36

Answer : original number = 36