Question

the difference of the digits of a 2-digit number is 1. five times the sum of the digits plus one is equal to the number. find the number

Answer 1

Let the digut in ten's place be x and digit in units place be y
x-y = 1 ; x = 1+y
5(x+y)+1 = 10x+y
5x+5y+1 = 10x+y
5y-y+1 = 10x-5x
4y+1 = 5x
4y+2 = 5(1+y)
4y+2 = 5+5y
2-5 = 5y-4y
-3 = y
x-y = 1
x-(-3) = 1
x+3 = 1
x = -2
Number = 10x+y = 10(-2)+(-3) = -20-3 = -23