2) The sum of the digits of a two-digit number is 12 . If the new number is formed by reversing the digits.is greater than the original number by 80. Find the original number
Answers
Answer:
Heyy mate, here's your answer
Solution - Let the digit in ones place be x So, the digit in tens place be 12 - X
Original no. = 10(12 - x) + 1(x)
= 120 - 10x + x
= 120 - 9x
New no. = 10(x) + 1(12 - x)
= 10x + 12 - X
= 9x + 12 [By reversing the digits]
According to Question,
New no. - Original no. = 54 (9x + 12) - (120 - 9x) = 54
= 9x + 12 - 120 + 9x = 54
= 18x - 108 = 54
= 18x = 54 + 108
= 18x = 162
= X = 162 / 18
X= 9
Required Numbers -
Original no. = 120 - 9x = 120 - 9(9)
= 120 - 81
= 39
New no. = 93 [:By reversing the digits]
Hence, the required number is either 39 or 93
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