Question

the sum of the digits of 2digit no. is 9..if we interchange the no. We get 9 more than original no..
find the no. with step by step solution
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Answer 1

Answer:

36 is the original number please add me as brainlist

Answer 2

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

Hence the required number is 36

Step-by-step explanation:

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