Calculating Sales Based on Commission Structures

Understanding how commission structures work is crucial for salespeople and managers alike. This article explores how to calculate total sales based on different commission rates. We'll use real examples to illustrate the process.

Example 1: Commission Structure for Sales

A company pays a 8.5% commission on sales up to Rs. 20,000 and a 7.0% commission on sales above Rs. 20,000. If the deposit from sales after commission deduction is Rs. 42,480, how much was the total sale?

To solve this, let's define some variables and break down the calculations step by step:

Define Variables

S - Total sales amount. 8.5% 7.0% Rs. 42,480 - Amount deposited after commission deduction.

The total commission can be calculated as:

Commission S - 42,480

Since the commission structure changes after Rs. 20,000, we need to consider the amount and commission in two parts:

If Sales (S) le; 20,000

Commission 0.085S S - 0.085S 42,480 0.915S 42,480 S 42,480 / 0.915 approx; 46,450.55

However, S cannot be more than 20,000, so this part of the solution is not valid.

If Sales (S) 20,000

Commission on the first Rs. 20,000 is Rs. 1,700 (0.085 * 20,000). Let x be the amount of sales above Rs. 20,000. Total sales 20,000 x. Commission on x is 0.07x.

The equation for total commission would be:

Total Commission 1,700 0.07x

The total sales minus total commission equals the deposit:

20,000 x - (1,700 0.07x) 42,480

Let's simplify this:

20,000 - 1,700 x - 0.07x 42,480

18,300 0.93x 42,480

0.93x 24,180

x 24,180 / 0.93 approx; 26,000

Therefore, the total sales of the salesman is:

S 20,000 26,000 46,000

Real-Life Application

In another scenario, a company pays a 9% commission on sales up to Rs. 15,000 and a 7% commission on sales above Rs. 15,000. If the company deposit is Rs. 32,250, what were the total sales?

Calculate Commission Structure

Given:

Commission on first Rs. 15,000 9% Commission on sales above Rs. 15,000 7% Deposit Rs. 32,250

Raise 7 to 100, i.e., 7 Rs 700 when 100 Rs 10,000:

Adjust the deposit by the difference in commission, i.e., 9 - 7 2, so Rs 2 Rs 300 increase in deposit. Therefore, Rs 300 increase in Rs 32,250 gives Rs 32,550.

If 93 Rs 32,550, then 100 Rs 35,000.

Thus, the total sales worth Rs 35,000 were made.