Question

The sum of the digits of a two-digit number is 9. When we interchange the digit it is found that the resulting new number is greater than the original number by 27. What is the two-digit number

Answer 1

Answer:

Let the digits of the original number be x and y

Hence, the original number is 10x + y (Assuming x to be the ten's digit and y to be the one's digit)

After interchanging the digits the new number will be 10y + x (After reversing, y becomes the ten's digit and x becomes the one's digit)

Condition 1: Sum of the digits is 9 ⇒ x + y = 9 --------- equation (i)

Condition 2: The number obtained by interchanging the digits is 27 greater than the earlier number.

⇒ New number = 27 + original number

⇒ 10y + x = 27 + (10x + y)

⇒ 10y + x = 27 + 10x + y

⇒ 10y - y + x - 10x = 27

⇒ 9y - 9x = 27

⇒ y - x = 3 -------- equation (ii)

By adding equation(i) and equation(ii):

x + y + y - x = 9 + 3

⇒ 2y = 12

⇒ y = 6

From equation(i): x + 6 = 9

⇒ x = 9 - 6 = 3

⇒ x = 3 and y = 6

⇒ The required number is 10x + y = 10 × 3 + 6 = 30 + 6 = 36

Thus, the required two-digit number is 36.

Answer 2

Step-by-step explanation:

Solution

Let unit digit is y and ten's digit is x.

Then, number will be 10x+y.

We are given,

x+y=9→(1)

When we interchange digits, number will be 10y+x

∴10x+y+27=10y+x

⇒9x−9y=−27⇒x−y=−3→(2)

Adding (1) and (2),

x+y+x−y=9−3⇒2x=6⇒x=3

∴3+y=9⇒y=6

So, two digit number will be = 3∗10+6=36