Sum of the digits of a two digits 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?
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Step-by-step explanation:
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Answer:
The two digit number is 36.
Step-by-step explanation:
Let,
Units digit = x
Tens digit = 9 - x
Original no. =
- 10 (9 - x) + x
- 90 - 9x
When we interchange the digits :
- 10x + (9 - x)
- 9x + 9
It is found that the resulting new number is greater than the original number by 27
⇒ 90 - 9x + 27 = 9x + 9
⇒ 90 + 27 - 9x = 9x + 9
⇒ 117 - 9x = 9x + 9
⇒ 117 - 9 = 9x + 9x
⇒ 108 = 18x
⇒ x = 108 / 18
⇒ x = 6
Units digit = 6
Tens digit = 9 - x
⇒ 9 - 6
⇒ 3
Tens digit = 3
∴ The two digit number is 36.
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