A number consists of two digits whose sum is 9.If 9 is subtracted from the number, the digits interchange their places.Find the number.
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54 is the answer . the sum the digits is 9 and when 9 is subtracted with 54 it is 45 and the digits are interchanged
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ab = 10 × a + b = 10a + b
ba = 10 × b + a = 10b + a
10a + b - 9 = 10b + a
10a - a - 9 = 10b - b
9a -9 = 9b
9 (a - 1)/9 = b
a - 1 = b
a - b = 1
Substituting
a + b = 9
a - b = 1
2a = 10
a = 10/2
a = 5
a - b = 1
5 - b = 1
5 - 1 = b
4 = b
ab = 54
ba = 10 × b + a = 10b + a
10a + b - 9 = 10b + a
10a - a - 9 = 10b - b
9a -9 = 9b
9 (a - 1)/9 = b
a - 1 = b
a - b = 1
Substituting
a + b = 9
a - b = 1
2a = 10
a = 10/2
a = 5
a - b = 1
5 - b = 1
5 - 1 = b
4 = b
ab = 54
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