Question

A two-digit number N is 'q' times the sum of its digits. The two-digit number formed by reversing the digits of N is 'p' times the sum of the digits.
Which of the following is equal to 'p'?

• A. (9 - q)
• B. (q + 1)
• C. (11 - q)
• D. (10 - q)

Answer 1

The correct option is C

(11 - q)

Let the number be xy.

Therefore, 10x + y = q(x + y)

Or (10 - q)x = y(q - 1)

Or $\frac{x}{y}=\frac{q-1}{10-q}$...(i)

If number xy is reversed, it is equal to 'p' times the sum of digits.

Then 10y + x = p(x + y)

Therefore, x(p - 1) = y(10 - p)

Or $\frac{x}{y}=\frac{10-p}{p-1}$...(ii)

Comparing, $\frac{10-p}{p-1}=\frac{q-1}{10-q}$

Solving, we get p = 11 - q.