# 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?PLZ SOLVE!!!!!!!!!!!!

Hi!

Let the tens digit be x and the ones digit be y.
x + y = 9  … (1)
Original number = 10x + y
Reverse number = 10y + x
Given, Reverse number = Original number + 27
∴10y + x = 10x + y + 27
⇒ 9y – 9x = 27
y – x = 3  … (2) y = 6
When y = 6,
x + 6 = 9  (Using (1))
x = 9 – 6 = 3
∴ Original number = 10x + y = 10 × 3 + 6 = 30 + 6 = 36

Cheers!

• 26

it is 36 and 63

• 1

Let the digits at tens place and ones place be x and 9 − x respectively.

Therefore, original number = 10x + (9 − x) = 9x + 9

On interchanging the digits, the digits at ones place and tens place will be x and 9 − x respectively.

Therefore, new number after interchanging the digits = 10(9 − x) + x

= 90 − 10x + x

= 90 − 9x

According to the given question,

New number = Original number + 27

90 − 9x = 9x + 9 + 27

90 − 9x = 9x + 36

Transposing 9x to R.H.S and 36 to L.H.S, we obtain

90 − 36 = 18x

54 = 18x

Dividing both sides by 18, we obtain

3 = x and 9 − x = 6

Hence, the digits at tens place and ones place of the number are 3 and 6 respectively.

Therefore, the two-digit number is 9x + 9 = 9 × 3 + 9 = 36

• 7

The same problem is in our textbook da, :P

• 2

but the chapter says to use only one variable????

• 0
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