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### Discussion :: Problems on Numbers

1. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

2.  A. 18 B. 24 C. 42 D. 81

Explanation :

Let the ten's and unit digit be x and$$\frac { 8 } {X }$$respectively.

Then,[10x +$$\frac { 8 } {X }$$]+ 18 = 10 x$$\frac { 8 } {X }$$+x

10x2 + 8 + 18x = 80 + x2

9x2 + 18x - 72 = 0

x2 + 2x - 8 = 0

(x + 4)(x - 2) = 0

x = 2.

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