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 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!
Here is the answer to your question.
 
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)
Adding (1) and (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
View Full Answer

it is 36 and 63

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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????

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