Question

the sum of digits of two digit number is 9 the number obtained by reversing the order of digits is 27 more than the original number find the original number​

Answer 1

Answer:

Original number  = 36

Step-by-step explanation:

Let the two digits of the number be 'a' and 'b'

Thus we can wirte the number in its value as - 10a+b  ....(1)

Given:

Sum of the two digits =

a + b = 9  ..... (2)

After reversing the digits, the value of the number can be written as

Reverse number = 10b + a  ... (3)

As per the given condition

Reverse number is 27 more than original number

∴ 10b + a = 10a + b + 27

Simplifying, we get,

9b - 9a = 27

∴ b - a = 3   ..... (4)

Adding eqn (2) & (4)... we get,

(a + b) + (b - a)  = 9 + 3

∴ 2b = 12

∴ b = 6

Puting b=6 in eqn (2),

a + 6 = 9

∴ a = 9-6

∴ a = 3

∴ Original number = 10a + b = 30 + 6 = 36

Original number = 36

Answer 2

the sum of digits of two digit number is 9 the number obtained by reversing the order of digits is 27 more than the original number find the original number

let say two digit number = xy

x + y = 9

value of number = 10x + y

reversed number = yx

value of reversed number = 10y + x

10y + x = 10x + y + 27

9y - 9x = 27

y - x = 3

y + x = 9

adding both

2y = 12

y = 6

x = 3

original number= 36