Question

Eight times a two digit number is equal to three times the number obtained by reversing theorder of its digits. If the difference between the digit is 5, find the number.

Answer 1

Let us assume, x and y are the digits of a two-digit number
Therefore, the two digit number = 10x + y and the reverse number is 10y + x
Given: 
8(10x + y) = 3 (10y + x)       This means y > x
80x + 8y = 30y + 3x
77x - 22y = 0
7x = 2y
x = (2/7)y ------------1
Also given:
y - x = 5 --------------2       Since y > x
Substitute the value of x from eqn 1 in eqn 2
y - (2/7)y = 5
7y - 2y = 35
5y = 35
y = 7
Therefore, x = 2/7 y = 2/7 * 7 = 2
The two digit number = 10x + y = (10 * 2) + y = 27

Answer 2

Answer:

Step-by-step explanation:

Let the number be 10x+y.

Given: 8(10x+y)=3(10y+x)

=>80x+8y=30y+3x

=>77x=22y

=>x=2y/7

Also, given that x-y=5 or y-x=5, let us take the second equation

=>y - 2y/7 =5

=>7y-2y=35

=>y=7, so x is 2. 

=> The number is 27.