1.

The number obtained by interchanging the two digits of a two-digit number is less than the original number by 18. The sum of the two digits of the number is 16. What is the original number?(a) 97       (b) 87(c) 79       (d) Cannot be determined(e) None of these

Answer» (a) Let the number be (10x + y)

Then, (10x + y) – (10y + x) = 18

9x – 9y = 18

x – y = 2 ...(i)

and, x + y = 16 ...(ii)

x = 9, y = 7

From equations (i) and (ii),

So, the number is (10 × 9 + 7) = 97


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