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1. A number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number its digits are interchanged. Find the number .
- A. 81
- B. 81
- C. 81
- D. 81
Answer: Option A
Explanation:
Let X and Y be the digits of decimal and unit places respectively. So, the number is 10X + Y. If 63 is subtracted from the number, it becomes 10Y + X.
Now, X + Y = 9 - - - - - - - (i)
Again, 10X + Y - 63 = 10Y + X
or, 10X - X + Y - 10Y = 63
or, 9X - 9Y = 63
or, X - Y = 63/9
or, X - Y = 7 - - - - - - (ii)
[(i) + (ii)]>> X + Y + X - Y = 9 + 7
or, 2X = 16
or, X = 8
So, 8 + Y = 9
or, Y = 9 - 8 = 1
So, the number is 81.
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