The sum of the digit of a number formed by interchanging the digits is greater than the orginal number by 54. find the orginal number
Answers
please correct your question and if question is
The sum of the digit of a two digit number is 12 if the new number formed by reversing the digit is greater than the original number by 54 find the original number , then
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
Check -
(i)...According to Question,
The sum of the digits of the two-digit number is 12
The digits are 3 and 9
∴ Sum of digits = 3 + 9 = 12
Hence, the require numbers are correct
(ii)... According to Question,
The new number is greater than Original number by 54
New number = 93
Original number = 39
∴ Clearly, 39 < 93
∴ 93 - 39 = 54
Hence, it is proofed that the required numbers are correct
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