The total emoluments of A and B are equal. However, A gets 65% of his basic salary as allowances and B gets 80% of his basic salary as allowances. What is the ratio of the basic salaries of and B?
Correct Answer: 12 : 11
Let the basic salaries of A and B be x and y respectively.
Now,
$$\eqalign{ & x + 65\% \,\,{\text{of }}x = y + 80\% \,\,{\text{of }}y \cr & \Rightarrow x + \frac{{ {65x} }}{{100}} = y + \frac{{ {80y} }}{{100}} \cr & \Rightarrow \frac{x}{y} = \frac{{180}}{{165}} \cr & \Rightarrow x:y = 12:11 \cr} $$
Now,
$$\eqalign{ & x + 65\% \,\,{\text{of }}x = y + 80\% \,\,{\text{of }}y \cr & \Rightarrow x + \frac{{ {65x} }}{{100}} = y + \frac{{ {80y} }}{{100}} \cr & \Rightarrow \frac{x}{y} = \frac{{180}}{{165}} \cr & \Rightarrow x:y = 12:11 \cr} $$