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Question

Sum of digits of a 2-digit number is 9. If the difference between the number and the one obtained when the digits are exchanged is 45. The number is .

A
72
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B
75
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C
70
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D
96
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Solution

The correct option is A 72
Let the digit in the units place be y and digit in the tens place be x. Then, the number is 10x + y and the number obtained on reversing the digits is
10y + x.

From question, x + y = 9-------(1)
and
10x + y - (10y + x) = 45
9x - 9y = 45
x - y = 5---------(2)

On adding equations (1) and (2),
we get

2x = 14

x = 7

On substituting x = 7 in equation (1), we get

7 + y = 9

y = 2

The required number is 72.

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