Question

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

Answer 1

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