The sum of the digit of two digit number is 17. if the number formed by reversing the dighit is less than the original number by 9 , find the original number
Answers
Answer:
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Step-by-step explanation:
Correct QuestioN :
The sum of the digits of a two digit number is 17. If the number formed by reversing the digits is more than the original number by 9. find the original number ?
To FinD :
Find the original number.
SolutioN :
Let's
Ten Place digit be x.
And Unit place digit be y.
Original number be 10x + y.
Reversing the number 10y + x.
☛ Case 1.
The sum of the digits of a two digit number is 17.
→ x + y = 17.
☛ Case 2.
If the number formed by reversing the digits is more than the original number by 9.
→ 10x + y + 9 = 10y + x.
→ 9x - 9y = 9.
→ x - y = - 1 ____ ( 2 )
✎ Now, Taking Equation ( 2 )
→ x - y = - 1.
→ x = y - 1 ____ ( 3 )
✎ Putting the value of x in Equation ( 1 )
→ x + y = 17.
→ y - 1 + y = 17.
→ 2y = 18.
→ y = 9.
✎ Putting the value of y = 9 in Equation ( 3 )
→ x = y - 1.
→ x = 9 - 1.
→ x = 8.
✡ Our Number become → 10x + y → 10(8) + 9
→ 80 + 9.
→ 89.
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Answer:
The sum of the digit of two digit number is 17. if the number formed by reversing the dighit is less than the original number by 9 , then the original number is 98
