the sum of the digit of a two digit number is 10 the number obtained by exchanging the digit exceeded the original number by 36 the original number is
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Step-by-step explanation:
Let's assume :
x = the 10's digits
y = units
Then the original number:
10x + y = two digit number
Now lets write down what's given in the problem:
x + y = 10
Re-written as: y= 10 -x (equation 1)
We are also told the number obtained by interchanging the two digits exceeds the number by 36:
interchanged = original + 36
10y + x = 10x + y + 36
9y = 9x + 36
y = x + 4
Now equate the above equation to equation 1
10 - x = x +4
2x = 6
x = 3
Now find y:
x+ y =10
y= 10 - 3
y = 7
Now we are required to find the original number. From above the equation of the original number is:
10x + y = 10(3) + 7 =37
The original number is 37
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