Question

A certain two – digit number is equivalent to five times the sum of the digits. It is found to be 9 less than the number formed when the digits are interchanged. Find the number.

Answer 1

xy =5(x+y)...(i)
xy +9 = yx....(ii)
10x + y = 5x + 5y
5x − 4y =0
10x + y + 9 = 10y + x
9x − 9y = −9
x−y=−1
x = −1 + y
5(−1+y)−4y = 0
−5 + 5y − 4y =0
y = 5
x = −1+ 5
x = 4
xy = 45