The sum of digits of a two digit number is a 8. the number obtained by interchanging the digits exceeds the given number by 18. find the given numbers.
Answers
Answer:
144
Step-by-step explanation:
8×18 = 144
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Answer:
The sum of the digits of a 2 digit number is 8.
Let the digits at 1s place be x. Then, the digits at 10s place is (8 - x)
Therefore original number = 10 (8 - x) + x
80 - 10x + x
80 - 9x
On interchanging the digits from 1s to 10s and vice versa
New number obtained = 10x + 8 - x
= 9x + 8
According to the statement, the number obtained by interchanging the digits exceed the original number by 18. The number to find out.
New number - Original number = 18
9x + 8 - (80 - 9x) = 18
9x + 8 - 80 + 9x = 18
18x - 72 = 18
18x = 18 + 72
18x = 90
x = 90 / 18
x = 5
Hence, the digit at 1s place is 5.
Now, digits at 10s place = (8 - 5) = 3.
Thus, the original number is 35 and the new number after interchanging the places of digits is 53.
Answer the original number is 35 and the new number is 53