Question

Sum of a two digit number is 9 if the digits are interchanged the new number is greater than the original number by 27

Answer 1

Step-by-step explanation:

units place X ; tens place Y

X+Y=9.....(1)

10X+Y= 10Y+X+27

9X-9Y=27

X-Y=3....(2)

from 1 & 2

2X=12

X=6...(IN 1)

6+Y=9

Y= 3

number- 36/63

Answer 2

Answer:

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Given

The sum of the two digits = 9

On interchanging the digits, the resulting new number is greater than the original number by 27.

Let us assume the digit of units place = x

Then the digit of tens place will be = 9–x

Thus the two-digit number is 109–x + x

Let us reverse the digit

the number becomes 10x + 9–x

As per the given condition

10x + 9–x = 109–x + x + 27

⇒ 9x + 9 = 90 – 10x + x + 27

⇒ 9x + 9 = 117 – 9x

On rearranging the terms we get,

⇒ 18x = 108

⇒ x = 6

So the digit in units place = 6

Digit in tens place is

⇒ 9 – x

⇒ 9 – 6

⇒ 3

Hence the number is 36