Eight times a two - digit number is equal to three times the number obtained by reversing the older of it's digits. If the difference between the digit is 5. Find the number
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Let us assume, x and y are the two digits of a two-digit number and y > x
Therefore, the two-digit number = 10x + y and reverse number = 10y + x
8 (10x + y) = 3 (10y + x)
80x + 8y = 30y + 3x
77x = 22y
7x = 2y -----------------1
Also given:
y – x = 5
x = y - 5 --------------2
Substitute the value of x from equation 2 in equation 1
7 (y - 5) = 2y
7y – 35 = 2y
5y = 35
y = 7
and x = y – 5 = 7 – 5 = 2
Therefore, the two-digit number = 10x + y = (10 * 2 + 7) = 27
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