Question

3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
found that the resulting new number is greater than the original number by 27. What
is the two-digit number?
nit
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Answer 1

Answer:

 36

Step-by-step explanation:

Let the two digit number be xy

unit place = y

ten's place = x

original number= 10x + y

When we interchange digits ,

unit place = x

ten's place = y

new number = 10y + x

According to the equation ,

10y + x = 10x + y + 27

9y - 9x =27

9(y - x) = 27

y - x = 3    -(i)

sum of digits = 9

x + y = 9   - (ii)

on adding (i) and (ii)

we get,

2y = 12

y = 6

putting value of y in (i)

we get,

6 - x = 3

- x = 3 - 6

x= 3  

original number = 10x + y

                           = 10(3) + 6

                           =  30 + 6

                           =  36

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