the sum of the digits of a two digit number is 12.if the new number formed by reversing the digits is greater than the original number by 54, find the original number .check your solution
Answers
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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