a number of two digits exceeds four times the sum of its digits by 6 and it is increased by 9 on reversing the digits. find the number

here,
The two digit number is 34

To find:

Number = ?

Solution:

Given : A number of two digits exceeds four times the sum of its digit by 6 and it is increased by 9 on reversing the digits.

Assume the 1st digit number as a & Second digit number as b.

Hence, the two digit number = 10a + b

Number of two digits exceeds four times the sum of its digit by 6  

10a + b = 4(a + b) + 6

10a + b = 4a + 4b + 6

6a - 3b = 6

2a - b = 2 ---------(1)

It is increased by 9 on reversing the digits.

10a + b + 9 = 10b + a

9a - 9b = -9

a - b = -1 ---------(2)

Solving the equations (1) & (2),

2a - b = 2  

a - b = -1  

a = 3

Replacing the value of a = 3 in 2a - b = 2

2(3) - b = 2

6 - b = 2

b = 4

Hence, the number = 10a + b

= 10(3) + 4

= 34