MATHEMATICS HIGH SCHOOL

in a two digit number the tens digit is 6 more than the units digit. if the digits are interchanged, the sum of the new and the original number is 132. Determine the original number.​

Answers

Answer 1
Answer:

Given:

In a two digit number the tens digit is 6 more than the units digit.

If the digits are interchanged, the sum of the new and the original number is 132.

To find:

The original number.

Solution:

Let the unit digit of the original number be x. So, the tens digit is (x+6) and the value of the number is:

m=(x+6)* 10+x* 1

m=10x+60+x

m=11x+60

If we interchange the digits, then the value of new number is:

n=x* 10+(x+6)* 1

n=10x+x+6

n=11x+6

The sum of the new and the original number is 132.

m+n=132

11x+60+11x+6=132

22x+66=132

22x=132-66

22x=66

Divide both sides by 22.

x=(66)/(22)

x=3

So, the unit digit of the original number is 3 and the tens digit is:

x+6=3+6

x+6=9

Therefore, the original number is 39.

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