Question

A salesman gets commission on total sales at \(9 \%\). If the sale is exceeded Rs. 10,000 he gets an additional commission at bonus of \(3 \%\) on the excess of sales over Rs. 10,000 . If he gers total commission of Rs. 1380 , then the bonus he received is: (a) Rs. 180 (b) Rs. 120 (c) Rs. 480 (d) data insufficient

Short answer

Based on the given information, a salesman earns a 9% commission on total sales and an additional 3% bonus commission on sales exceeding Rs. 10,000. We are asked to find the bonus amount he received if his total commission was Rs. 1380. After setting up and solving the necessary equations, we find that the total sales were Rs. 14,000, and the bonus amount he received was Rs. 120.

Step-by-step solution

Understand the given information

A salesman earns a 9% commission on total sales. If the sales exceed Rs. 10,000, he earns an additional bonus commission of 3% on the excess amount. His total commission is Rs. 1380. We need to find the bonus he received.

Analyze the problem

As he has a total commission of Rs. 1380, we need to find out what part of it is regular commission and what part is bonus commission. Let's denote total sales as 's' and the bonus amount as 'b'.

Set up the equations

Let's set up two equations based on the available information: 1. Regular commission: \(\displaystyle \frac{9}{100}s\) 2. Bonus commission: \(\displaystyle \frac{3}{100}( s-\text{10,000})\) The total commission is the sum of the regular commission and the bonus commission: \(\displaystyle \frac{9}{100}s +\displaystyle \frac{3}{100}( s-\text{10,000})=\text{1,380}\)

Solve for the total sales 's'

To find the value of 's', we can combine the two parts of the equation: \(\displaystyle \frac{12}{100}s -\text{300} =\text{1,380}\) Now, we can solve for 's': \(s=\frac{\text{1,680}}{0.12}= \text{14,000}\) So, the total sales amount is Rs. 14,000.

Calculate the bonus amount 'b'

Now that we know the total sales, we can calculate the bonus amount using the equation for bonus commission: \(b = \displaystyle \frac{3}{100}(s-\text{10,000})\) \(b = \displaystyle \frac{3}{100}(\text{14,000}-\text{10,000})\) \(b = \displaystyle \frac{3}{100}(\text{4,000})\) \(b = \text{120}\) The bonus amount he received is Rs. 120. So, the correct answer is (b) Rs. 120.

Key concepts

Percentage Calculation

Understanding percentage calculation is essential, especially when it comes to commissions and bonuses, as seen in the exercise of the salesman. A percentage represents a fraction of 100 and is used to determine proportions or parts of a whole. For example, if a salesman gets a commission at a rate of 9%, it means he earns 9 parts out of every 100 whether in money or sales volume.

To calculate a percentage of a business number, multiply the number by the percentage given (in decimal form). For example, if the total sales are Rs. 14,000 and the commission is 9%, the amount earned from the commission can be calculated as follows:

• Commission = 9/100 * 14,000 = Rs. 1,260

Percentage calculation is incredibly useful in various real-life situations, not just in sales and commissions, but also in determining interest rates, tax, and discounts.

Additional Commission

In the scenario with the salesman, additional commission refers to the bonus he receives when his sales exceed a certain threshold. This bonus incentivizes higher sales as it leads to extra earnings on top of the standard commission.

The exercise specifies that if the salesman exceeds Rs. 10,000 in sales, he earns an extra 3% commission on the amount over Rs. 10,000. This means that the more the sales exceed this threshold, the more significant the bonus will be.

• Calculation of additional commission: Bonus = 3% of (Sales - Rs. 10,000)

This concept is advantageous in sales careers because of the encouragement it provides to push beyond minimum targets, thereby increasing both sales volume and earning potential.

Sales Threshold

A 'sales threshold' is a set level of sales which acts as a benchmark. Once exceeded, certain benefits, such as additional commissions, come into play. In our problem, the threshold is Rs. 10,000. This is the point at which any further sales amount attracts bonus commission.

Understanding and hitting sales thresholds is crucial for salespeople, as it can be a significant factor in maximizing earnings. Reaching this level implies that not only will you earn a regular commission on your total sales but also an extra incentive for exceeding the threshold.
The threshold in many business scenarios is strategically set to stimulate higher performance and greater revenue generation. It is designed to align the interests of the salesperson or worker with those of the company.

Mathematical Problem Solving

Mathematical problem-solving skills are crucial for effectively tackling and understanding exercises like the commission calculation of a salesman. This involves breaking down the problem, forming equations, and systematically solving for unknowns.

In the example problem, the process is straightforward once the equations are set:

• Determine regular and bonus commission formulas.
• Set up an equation that sums these to give the total known commission.
• Solve the equation to find the total sales amount.
• Use the total sales amount to calculate the additional bonus.

Problem-solving isn't just crucial for academic exercises; it's a vital skill in daily life and the business world. Practicing structured approaches to problems enhances analytical capabilities, helping to find efficient and accurate solutions.