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sum of the digits of a two digit number is 12 new number formed by reversing the digit is greater than the original number by 54 find the original number |
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Answer» Step-by-step explanation: => 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] ∴ the required number is EITHER 39 or 93 ∴ Sum of digits = 3 + 9 = 12 The new number is greater than Original number by 54 verification :- New number = 93 Original number = 39 ∴ 39 < 93 ∴ 93 - 39 = 54 |
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