Question

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

Answer 1

Answer:

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Step-by-step explanation:

Let's set up a system with two variables: x = tens place of our answer, y = units place of our answer.

Digit sum of a two digit number is 6:

x+y=6

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

10y+x=10x+y-18

Now let's solve:

y=6-x

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

So our original number was 42. Sum of digits is 6. Swap the order of the digits to make 24, and you have a number 18 less than the original number.

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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