The sum of the digits of a 2-digit number is 11. If we add 45 to the number, the new number obtained is a number formed by the interchange of the digits. What is the number?
Answers
Answer:
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Step-by-step explanation:
Let the first digit of number be x and second digit of number be y.
So the number will look like xy Or 10*x + y
x + y = 11 and,
10*x + y + 45 = 10*y + x
Putting, y = 11 - x in above equation
10*x + (11 - x) + 45 = 10*(11 - x) + x
10x + 11 - x + 45 = 110 - 10x + x
18x = 54
x = 3
And as y = 11 - x, so y = 8
Therefore the number is 38.
Thank you
Step-by-step explanation:
Let the ten's place be = x
Let the unit place be = y
original number = 10x + y
reversing number = 10y + x
Case = 1.
The sum of digit of a two digit number is = 11
=> x + y = 11 ...... (1)
Case = 2.
If 45 is added to the number the new number
obtained is a number formed by the
interchanging of its digit.
=> 10x + y + 45 = 10y + x
=> 9x - 9y = -45
=> x - y = -5 ..... (2)
From equation (1) and (2) we get,
=> 2x = 6
=> x = 3
put the value of x = 3 in equation (1)
we get,
=> 3 + y = 11
=> y = 8
Therefore,
original number = 10x + y
=> 10(3) + 8 = 38
original number = 38