A number consists of two digits. The sum of the digits

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A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

1. 63
2. 72
3. 81
4. 90

Correct Option: B

Let two digit number be xy.
Now sum of digit is 9
∴ x + y = 9 ....(i)
and when ‘45’ is subtracted from number then digit gets interchanged
∴ 10x + y – 45 = 10y + x
∴ x – 5 = y
x – y = 5 ....(ii)
Now solving equation (i) and (ii) we get
x = 7 and y = 2
Hence the number is 72.