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The sum of the digits of a two digit number is 14 if the number formed by reversing the digits is less than the original number by 18 find the original numbers

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Kishore answered 4 year(s) ago

The sum of the two digit number is 12.

the sum of the two digit number is 12. if the new no. formes by reversing yhe digit is greater than yhe originol no. by 54. find the originol no.

Class-VIII Maths

person

Asked by Sheetal

Sep 23

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person

Subhikshasampath , Student

Member since Aug 01 2013

The number is 39.
3+9=12
The reverse of 39 is 93. It is greater by 54.

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Kishore , Student

Member since Dec 10 2008

Given sum of the digits is 12
Let the digits in ones place be x
Hence the digit in tens place is (12 – x)
The original number = 10(12 – x) + x = 120 – 9x
Number formed by reversing the digits = 10x + (12 – x)  =  9x + 12
Given that number formed by reversing the digits is 54 greater than the original number.
⇒ 9x + 12 = (120 – 9x) + 54 = 174 – 9x
⇒ 18x = 174 – 12 = 162
∴ x = 9
The original number = 120 – 9x = 120 – 9(9) = 39

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