Question

the sum of the digit of a two digit number is 15 if the number formed by reversing the digit is less than the original number by 27 find the number​

Answer 1

Answer:

96

Step-by-step explanation:

Let the digits of the number be x and y

Sum of the digits = 15

x + y = 15

x = 15 - y -----(1)

Original number = 10(x) + y = 10x + y ----(2)

New number when the digits are reversed = 10(y) + x  = 10y + x

New number is less than the original number by  27

It means : Difference between original number and new number = 27

Equation formed :

10x + y - (10y + x) = 27

10x + y -  10y  -  x = 27

9x - 9y  = 27

9(15 - y) - 9y = 27 (From (1))

135 - 9y - 9y = 27

165 - 18y = 27

135 - 27 = 18y

108 = 18y

108/18 = y

y = 6

Substitute the y = 6 in 1 to get the value of x

x = 15 - 6

x = 9

Substitute x = 9 , y = 6 in (2) to find the number

10(9) + 6 = 90 + 6 = 96

So, 96 is the required number.