The sum of the digits of a two digit number is 7.If 9 is added to the number, digits interchange their place. Find the number.

July 1, 2021

By Vivian

1 thought on “The sum of the digits of a two digit number is 7.If 9 is added to the number, digits interchange their place. Find the number.<br”

1. Answer:

   34

   Step-by-step explanation:

   Let the first digit be x.

   since sum is 7, implies second digit will be 7-x

   Now, place value of x at tens place is 10x.

   ( example: 29 = 20 +9. means digit 2 is multiplied by its place 2×10 )

   so the original number is 10x + 7-x

   => 10x – x + 7 = 9x +7

   Original Number = 9x + 7

   If these digits are interchanged then: 7-x will be at tens place & x will be at ones place.

   => new number will be: 10(7-x) + x

   => 70 – 10x +x

   combining the like terms we get: 70 – 9x

   New Number = 70 – 9x

   according to the question: if 9 is added to the number

   => 9x + 7 + 9 = 70 -9x

   equation is formed. Now combining the like terms we get:

   9x + 16 = 70-9x

   9x + 9x = 70 -16

   18x = 54

   => x = 54/18 = 3

   => first digit = 3 & second digit = 7-x = 7-3 =4

   hence the number is 34

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