A number of two digits exceed four times the sum of its digits by 6 and it is increased by 9 on reversing its digits. Find the number

let the unit digit of the number be x and ten's digit be y.

the number = 10y+x

10 y+x = 4(x+y) + 6

10 y + x - 4x - 4y = 6

- 3x +6y = 6

- x + 2y = 2...............(1)

the number by reversing its digit = 10 x + y

10y+x = 10x+y + 9

-9x + 9y = 9

-x + y = 1.........(2)

subtracting eq (2) from eq(1):

y = 1 and x = 0

thus the number is 10.

hope this helps you.