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 A and B ?
Correct Answer: 12 : 11
Let the basic salaries of A and B be Rs. x and Rs. y respectively.
Then,
= x + 65% of x = y + 80% of y
$$\eqalign{ & \Rightarrow \frac{{165}}{{100}}x = \frac{{180}}{{100}}y \cr & \Rightarrow 165x = 180y \cr & \Rightarrow \frac{x}{y} = \frac{{180}}{{165}} = \frac{{12}}{{11}} \cr & \therefore {\text{Required ratio}} \cr & = 12:11 \cr} $$
Then,
= x + 65% of x = y + 80% of y
$$\eqalign{ & \Rightarrow \frac{{165}}{{100}}x = \frac{{180}}{{100}}y \cr & \Rightarrow 165x = 180y \cr & \Rightarrow \frac{x}{y} = \frac{{180}}{{165}} = \frac{{12}}{{11}} \cr & \therefore {\text{Required ratio}} \cr & = 12:11 \cr} $$