Rihaan analyzed the monthly salary figures of five vice presidents of his company. All the salary figures are in integer lakhs. The mean and the median salary figures are Rs. 8 lakhs, and the only mode is Rs. 11 lakhs. Which of the options below is the sum (in Rs. lakhs) of the highest and the lowest salaries, assuming that lowest salary is an even integer in lakhs?

Rihaan analyzed the monthly salary figures of five vice presidents of his company. All the salary figures are in integer lakhs. The mean and the median salary figures are Rs. 8 lakhs, and the only mode is Rs. 11 lakhs. Which of the options below is the sum (in Rs. lakhs) of the highest and the lowest salaries, assuming that lowest salary is an even integer in lakhs? Correct Answer 15

The mean salary of the five vice presidents is Rs. 8 lakhs.

So, the sum of their salaries = 5 × 8 = 40 lakhs.

Let their salaries in ascending order be a, b, c, d and e.

a + b + c + d + e = 40

The median salary is Rs. 8 lakhs

So, c's salary is Rs. 8 lakhs.

 The only mode is Rs. 11 lakhs.

So, Rs. 11 lakhs salary is drawn by the maximum number of VPs.

C's salary is Rs. 8 lakhs

So, d and e have to draw Rs. 11 lakhs each

a + b + 8 + 11 + 11 = 40

a + b = 10

Their salaries are in integer lakhs.

Therefore, a can draw Rs. 3 lakh and b can draw Rs. 7 lakh or a can draw Rs. 4 lakh and b can draw Rs. 6 lakhs or a and b can both draw Rs. 5 lakhs each.

However, there is only one mode. So, a and b cannot draw Rs. 5 lakhs each and lowest salary cannot be odd number.

So, a draws Rs. 4 lakhs (the least salary) and e draws Rs.11 lakhs (the highest salary).