Question

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? (How do you find the answer using two variables? Please explain)

Answer 1

Answer:

36

Step-by-step explanation:

The new number is greater than the old number by 27, i.e. Adding the two equations, we get 2y = 12 or y = 6. Thus, x = 3. Therefore, the original number is 36.

Answer 2

Answer:

36

Step-by-step explanation:

Assume the tens digit be x and ones digit be y.

Number = 10x + y

Sum of the digits of a two digit number is 9.

→ x + y = 9

→ x = 9 - y -------- (1)

When we interchange the digits, it is found that the resulting new number is greater than the original number by 27.

• Original number = 10x + y
• Interchanged number = 10y + x

As per given statement,

→ 10x + y = 10y + x - 27

→ 10x - x + y - 10y = -27

→ 9x - 9y = -27

→ x - y = -3

→ 9 - y - y = -3

→ -2y = -12

→ y = 6

Substitute value of y in (1)

→ x = 9 - 6

→ x = 3

Hence, the original number is 36 (30+6).