Question 30

A number of two digits is equal to ‘k’ times to the sum of these digits. If the places of the digits are mutually exchanged, the new formed number is equal to the sum of these digits multiplied by which one of the following options ?

Solution

Let the number be xy. So 10 x +y = k (x + y)

11 - k = 11- $$ \frac{10x+y}{x+y}$$ = $$\frac{11x + 11y - 10x - y}{x+y}$$

= $$ \frac {10y + x}{x+y}$$ which is inverse of the number divided by the sum of the digits.

Hence the required factor is 11 - k

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