Question

The sum of the digits of a 2-digit number is 6. On reversing its digits, the number is 18 less than the original number. Find the number.​

Answer 1

The sum of the digits is 6 (given in the question)

Let the digit at one's place be x

Let the digit at ten's place be (6-x).

Reverse the digits and you get 18 less than the original value:

10y+x=10x+y-18

10(6-x)+x=10x+(6-x)-18

60-10x+x=10x+(6-x)-18

60-9x=9x-12

72=18x

x=4

y=6-4

y=2

Number = 24

Answer 2

Given : The sum of the digit of a 2- digit number is 6. On reversing its digits, the number is 18  less than the original number

To Find : the number

Solution:

Let say original number = AB

A + B = 6

Reversed number = BA

On reversing its digits, the number is 18 less than the original number

10B + A  = 10A + B - 18

=> 9(A - B)   = 18

=> A  -  B = 2

2A  = 8

=> A = 4

    B = 2

Number = 42

Verification :

4 + 2 = 6

24 = 42 - 18

42 is the number whose sum of the digit  is 6 and on  reversing its digits, the number is 18 less than the original number

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