Question

The sum of the digits of a two digit number is 7. If we interchange the digits, then the resulting number is 9 less than the original number, then what is the digit?​

Answer 1

Numbers can be,

10, 21, 32, 43, 54, 65, 76, 87, 98

Step-by-step explanation:

QUESTION :-

The sum of the digits of a two digit number is 7. If we interchange the digits, then the resulting number is 9 less than the original number, then what is the number?

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SOLUTION :-

Let the number's tens digit = x

and, ones digit = y

So,

The original number will be 10x + y

And,

number after interchanging digits = 10y + x

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A.T.Q.

Original number - resulting number (interchanging digits) = 9

=> 10x + y - (10y + x) = 9

=> 10x + y - 10y - x = 9

=> 10x - x + y - 10y = 9

=> 9x - 9y = 9

=> 9(x - y) = 9

=> x - y = 9/9

=> x - y = 1

Now,

You can put any single digit number as x, and y as 1 less than x. You will get the number.

Like :-

x = 3 ; y = 2

=> original number = 10x + y = 10(3) + 2 = 30+2

= 32

number by interchanging digits = 23 , which is 9 less than original.

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CONCLUSION :-

The possible numbers are,

• 10
• 21
• 32
• 43
• 54
• 65
• 76
• 87
• 98

If you interchange the digits (of following numbers), the resulting number will be 9 less than original.

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Hope it helps.

#BeBrainly :-)