the sum ofthedigitsofatwo digitnumberis 16. if the new number forms by reversing the digits is greater than the original number by 18. find the original number
Answers
EXPLANATION.
- GIVEN
The sum of digit of two digit number = 16
the new number is formed by reversing the
digit is greater than the original number
by = 18
Find the original number.
According to the question,
Let the ten's place = x
Let the unit place = y
Original number = 10x + y
reversing number = 10y + x
Case = 1.
The sum of digit of two digit number = 16
=> x + y = 16 ......(1)
Case = 2.
the new number is formed by reversing the
digit is greater than the original number
by = 18.
=> 10y + x - ( 10x + y) = 18
=> 10y + x - 10x - y = 18
=> 9y - 9x = 18
=> y - x = 2 ...... (2)
From equation (1) and (2) we get,
=> 2y = 18
=> y = 9
put the value of y = 9 in equation (1)
we get,
=> x + 9 = 16
=> x = 7
Therefore,
Original number = 10x + y
=> 10(7) + 9 = 79
The number = 79
Answer:
Number is 79
Step-by-step explanation:
Assume ten's digit number be x and one's digit number be y.
The sum of the digits of a two digit number is 16.
→ x + y = 16
→ x = 16 - y ......................(1)
If the new number forms by reversing the digits is greater than the original number by 18.
Original Number: 10x + y and Reversed Number: 10y + x
→ 10y + x - ( 10x + y) = 18
→ 10y + x - 10x - y = 18
→ 9y - 9x = 18
→ y - x = 2
→ x = y - 2 .......................(2)
On comparing (1) & (2) we get,
→ 16 - y = y - 2
→ 18 = 2y
→ y = 9
Substitute value of y in (2)
→ x = 9 - 2
→ x = 7
Hence, the number is 79 [10(7)+9].