A number consist of two digit whose sum is8. if 18is added to the number the digit are interchanged find the number
Answers
Answer:
The Orignal Number is 35.
Step-by-step explanation:
Given :
Sum of digits = 8
The digits interchange when = 18 is added to the original number
To find :
The number
Solution :
✯
Let the digits be,
- Units place as y
- Tens place as 10(8 - y)
⇒ 10(8 - y) + y
⇒ 80 - 10y + y
⇒ 80 - 9y --------- (Orignal Number)
✯
Let the digits be,
- Units place as (8 - y)
- Tens place as 10(y)
⇒ 10(y) + (8 - y)
⇒ 10y + 8 - y
⇒ 9y + 8 -------- (Number with reversed digits)
✯
Number gets reversed when 18 is added.
⇒ (80 - 9y) + 18 = 9y + 8
⇒ 98 - 9y = 9y + 8
⇒ - 9y - 9y = 8 - 98
⇒ 18y = 90
⇒ y = 90/8
⇒ y = 5
✯
⇒ 80 - 9y
⇒ 80 - 9(5)
⇒ 80 - 45
⇒ 35
The Orignal Number is 35.
Answer:
Step-by-step explanation:
Given :-
Sum of 2-digit number = 8
If 18 is added to the number, the digits change their places.
To Find :-
The Number
Solution :-
Let one of the number be x
And the other number be 8 - x
According to the question,
⇒ 10x + (8 - x) + 18 = 10(8 - x) + x
⇒ 10x + 8 - x + 18 = 80 -10x + x
⇒ 9x + 26 = 80 - 9x
⇒ 9x + 9x = 80 - 26
⇒ 18x = 54
⇒ x = 54/18
⇒ x = 3
One Number = x = 3
Other number = 8 - x = 8 - 3 = 5
Hence, the number is 35.