A salesman receives a commission of 9% on his total sales. If his sales exceed Rs. 10,000, he also earns an additional bonus commission of 3% on the portion of sales above Rs. 10,000. If his total commission from both parts together is Rs. 1,380, how much bonus (in rupees) did he receive on the excess sales?

Difficulty: Medium

Correct Answer: Rs. 120

Explanation:


Introduction:
This percentage word problem tests understanding of commission calculations with a base rate and an additional bonus rate on sales beyond a threshold. Such questions are common in aptitude exams to check how well a candidate converts a verbal description of a commission structure into algebraic equations and then solves for the unknown quantity, which in this case is the amount of bonus received.

Given Data / Assumptions:
Total sales value is unknown and is represented by S rupees.
Base commission rate is 9% on the entire sales S.
If sales exceed Rs. 10,000, an extra bonus commission of 3% is paid on the amount above Rs. 10,000.
Total commission earned from base commission plus bonus is Rs. 1,380.
We assume the salesman definitely exceeded Rs. 10,000 in sales because a bonus is mentioned as part of the total commission.

Concept / Approach:
The key idea is to express the total commission as the sum of two components: the regular commission on total sales and the bonus commission on sales beyond Rs. 10,000. Once we write this as an equation in S, we can solve for S and then compute the bonus amount, which is 3% of the excess sales. This is a standard linear equation in one variable based on percentage calculations.

Step-by-Step Solution:
Let total sales be S rupees. Regular commission = 9% of S = 0.09 * S. Bonus commission is applicable on excess sales over Rs. 10,000, so excess = S - 10000. Bonus commission = 3% of (S - 10000) = 0.03 * (S - 10000). Total commission = regular commission + bonus commission. So 0.09 * S + 0.03 * (S - 10000) = 1380. Simplify: 0.09 * S + 0.03 * S - 0.03 * 10000 = 1380. This gives 0.12 * S - 300 = 1380. Add 300 to both sides: 0.12 * S = 1680. So S = 1680 / 0.12 = 14000 rupees. Excess over Rs. 10,000 = 14000 - 10000 = 4000 rupees. Bonus commission = 3% of 4000 = 0.03 * 4000 = Rs. 120.
Verification / Alternative check:
We can verify by computing both parts of the commission separately. Regular commission at 9% of Rs. 14,000 is 0.09 * 14000 = Rs. 1,260. Bonus commission is Rs. 120, so total commission is 1260 + 120 = Rs. 1,380, which matches the given total commission in the question. This confirms that the sales figure and bonus amount are correct.

Why Other Options Are Wrong:
Rs. 180, Rs. 240, Rs. 300 and Rs. 360 correspond to larger excess sales values or incorrect percentage applications. If any of these were correct, the recomputed total commission would not match Rs. 1,380. These values typically come from misreading the bonus as 3% of total sales or from arithmetic mistakes in solving the equation.

Common Pitfalls:
A very common mistake is to apply the 3% bonus on the entire sales amount instead of only the portion above Rs. 10,000. Another error is to forget to add the base commission and bonus commission before equating to the total commission. Sometimes students also mis-handle decimal percentages like 0.09 and 0.03 and end up with a wrong equation for S. Careful reading of the words “on the excess of sales over Rs. 10,000” is crucial.

Final Answer:
The bonus received by the salesman on the excess sales is Rs. 120.

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