Question

Ques 3. The sum of the digit number is 9. The number obtained by reserving the digits is 9 less than the original number. Find the number.

Answer 1

CORRECT QUESTION:-

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• The sum of the digits of a two digit number is 9. The number obtained by reversing the digits is 9 less than the original number. Find the number.

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Solution:-

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ANSWER:-

• Number at units place is 4.
• Number at ten's place is 5.
• Original number is 54.

GIVEN:-

• Sum of the two digit number = 9
• Number obtained by reversing the digit is less = 9

TO FIND:-

• Find the number:-

SOLVING STEP BY STEP:-

• Let the number at the one's place be x.
• Let the number at the ten's place be (9 - x).
• Original Number:-
• Ten's × 10 + Units
• (9 - x) × 10 + x
• 90 - 10x + x
• 90 - 9x
• After Interchanging:-
• Ten's = x
• One's = 9-x
• x × 10 + 9 - x
• 10x + 9 - x
• 9x + 9

ACCORDING TO THE QUESTION:-

• (9x + 9) + 9 = 90 + 9x
• 9x + 18 = 90 - 9x
• 9x + 9x = 90- 18
• 18x = 72
• x =72/18
• x = 72/18 = 4
• x = 4
• Hence, the number at the units place is 4.
• Hence, the number at the ten's place is 5.
• So the original number is 54, by reversing it becomes 45 which is 9 less than 54.

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