The sum of the digits of a 2-digit number is 11. The number obtained by
interchanging the digits exceeds the original number by 27. Find the number.
Answers
Let the digit in the ones place be y.
Let the digit in the tens place be x.
Original number = (x*10)+y
Given, x + y = 11
i.e. x =11 - y
When the digits are interchanged, the new number = (y*10)+x.
Given that,
New number=Original number + 27
(y*10) + x = (x*10) + y + 27
Substituting x = 11 - y in the above equation,
(y*10) + 11 - y = [(11 - y) *10] + y + 27
10y + 11 - y = 110 - 10y + y + 27
10y - y + 10y - y = 110 + 27 - 11
18y = 126
y = 7
Substituting y=7 in x=11-y
x = 11 - 7 = 4
Original number = (x*10) + y = (4*10) + 7 = 40+7 = 47
Original number is 47.
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Answer:
Step-by-step explanation:
Let the digit in the ones place be y.
Let the digit in the tens place be x.
Original number = (x*10)+y
Given, x + y = 11
i.e. x =11 - y
When the digits are interchanged, the new number = (y*10)+x.
Given that,
New number=Original number + 27
(y*10) + x = (x*10) + y + 27
Substituting x = 11 - y in the above equation,
(y*10) + 11 - y = [(11 - y) *10] + y + 27
10y + 11 - y = 110 - 10y + y + 27
10y - y + 10y - y = 110 + 27 - 11
18y = 126
y = 7
Substituting y=7 in x=11-y
x = 11 - 7 = 4
Original number = (x*10) + y = (4*10) + 7 = 40+7 = 47
Original number is 47.