Let the two digits be represented by 10x + y, where x and y are the digits.
Given that the sum of the digits is 10:
x + y = 10 (1)
When the digits are reversed, the new number is 10y + x.
Given that the new number is less than the original number by 18:
10x + y - (10y + x) = 18
9x - 9y = 18
x - y = 2 (2)
Now we have a system of two equations:
x + y = 10
x - y = 2
Adding the two equations together, we get:
2x = 12
x = 6
Substitute x = 6 into equation (1):
6 + y = 10
y = 4
Therefore, the number is 64.
A two digit number is such that the sum of digitis ten if the digits are reversed the new number formed is less than original number by 18 find the number
3 answers
just for future reference, if the reversed digits for a number that is less by 9n, the the digits differ by n.
That is correct! Thank you for pointing that out. If the reversed digits of a two-digit number are less than the original number by a multiple of 9, the digits will differ by that multiple. This is because reversing the digits causes a change in the value of x 10 times and the value of y 1 time, resulting in the difference between the two numbers being a multiple of 9.