The total emoluments of two persons are the same, but one gets allowances to the extent of 65% of his basic pay and the other gets allowances to the…

Correct Option

Let the basic pay of the former person be x₁ and the basic pay of the latter person be x₂.

The former person receives allowances equivalent to 65% of their basic pay. Therefore, the total emoluments for the former person are calculated as:

$$= x_{1} + \frac{65}{100}x_{1} = \frac{165}{100}x_{1}$$=x1​+10065​x1​=100165​x1​

The latter person receives allowances equivalent to 80% of their basic pay. Consequently, the total emoluments for the latter person are:

$$= x_{2} + \frac{80}{100}x_{2} = \frac{180}{100}x_{2}$$=x2​+10080​x2​=100180​x2​

As per the problem statement, the total emoluments of both persons are identical. Thus, we can equate their total emoluments:

$\frac{165}{100}x_{1} = \frac{180}{100}x_{2}$100165​x1​=100180​x2​

To determine the ratio of the basic pay of the former to the basic pay of the latter ($x_1 : x_2$x1​:x2​), we rearrange the equation:

$$\frac{x_{1}}{x_{2}} = \frac{180}{100} \times \frac{100}{165} = \frac{12}{11}$$x2​x1​​=100180​×165100​=1112​

Therefore, the ratio of the basic pay of the former to the basic pay of the latter is 12:11.

Incorrect Options

Options (1) 16:13, (2) 5:4, and (3) 7:5 are incorrect. These ratios do not satisfy the condition that the total emoluments of both individuals are equal, given that their allowances are 65% and 80% of their respective basic pays. The accurate calculation, derived from equating the total emoluments, demonstrates that a ratio of 12:11 is necessary for the stated condition to hold true.