Question

Four times a certain two digit number is seven times the number obtained on interchanging its digits. If the difference between the digits is 4; find the number.

Answer 1

Let x be the number at the ten's place.
and y be the number at the unit's place.
So, the number is 10x + y.

Four times a certain two-digit number is seven times
the number obtained on interchanging its digits.
⇒ 4( 10x + y ) = 7( 10y + x )
⇒ 40x + 4y = 70y + 7x
⇒ 33x - 66y = 0
⇒ x - 2y = 0                  ....(1)

If the difference between the digits is 4, then
⇒ x - y = 4                     ...(2)
Subtracting equation (1) from equation (2), we get :
         x - y = 4
    -   x - 2y = 0  
       -   +      -     
              y = 4
Subtracting y = 4 in equation (1), We get
x - 2(4) = 0
⇒ x = 8
∴ The number is 10x + y = 10(8) + 4 = 84.