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Quantitative Aptitude > Profit and Loss > Dishonest Dealers and Faulty Weights
Profit and Loss

Dishonest Dealers and Faulty Weights

Have you ever met a Dishonest dealer or a dishonest shopkeeper? So far we have seen many concepts in the section on Profit and loss. All of the formulae we use are for trading practices that are transparent and honest. But this is not always true. Suppose you are in the Income Tax Bureau or a bank manager who is inspecting a business. Can you take a look at their records and figure out if they are hiding something? In the below space we will see how this dishonesty in trade works. We will modify various formulae and use several others to fix these instances of cheating. Let us see further below!

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Dishonest Dealers and Faulty Weights

In the profit an loss section, our formula and rules will work only for those cases where the trade is fair and simple. However, you will also have to be ready for the false scale dealers which we will see here. The profit or loss of the dealer will depend on the actual selling price.

For example, let us say that a dealer sells apples as Rs 100/kg. For each sale he makes, the dealer removes an apple from the final stock. If the average cost of an apple is Rs 20, he should make an additional Rs 20 on each sale that he makes. This will be in addition to his actual profit or the legal profit. So we need a mechanism or a set of formulae to correctly predict the gain percentage of the dishonest dealers. in the following sections, we will see the concepts that are essential and we will also state and practice the formula for calculating the gain percentage.

Dishonest Dealers

Dishonest Dealer

The dishonest dealer is one who doesn’t sell his product in the welfare of the customer. This type of dealer changes the weight or marks up the price too high so as to increase his margins. Another dishonest practice is that the dealer can list a very high price and then sell the item at a considerable discount. This is also a dishonest trading practice. Let us get a quantitative idea of this concept.

Suppose G% represent the overall gain percentage or the overall gain that a dishonest dealer makes through selling their product or item. Let x be the percentage loss or the percentage gain (whichever be the case). Therefore, we can write [(100 + G)/(100 + x)] = (True value)/(False value). We can have another formula as stated below.

If a trader professes to sell his goods at cost price but uses false weights, then:

Gain% (Percentage gain) = [(Error)/{(True Value) – (Error)}]×100%. This is the formula that we shall use in solving the examples from this section. Let us see some solved examples that will help us get a better idea about the application of this formula.

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Solved Examples For You

Example 1: A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 gms instead of a kg weight. Find the gain of this dishonest person in percent.

A) 5(3/4)%                 B) 4.167%                      C) 5(1/6)%                  D) None Of These

Answer: Here we will use the second formula that we have. We know that:

Gain% (Percentage gain) = [(Error)/{(True Value) – (Error)}]×100%.

Here the “error” is the difference between the true value and the fabricated value. Thus error = 1000 gm (1 kg) – 960 gms = 40 gms. Thus substituting this in the formula for the dishonest dealer, we have:

Gain% = [(Error)/(True Value) – (Error)] × 100% = 4(1/6)% = 4.167%. Hence the correct option is B) 4.167%. (74, 78,

Example 2: A dishonest shopkeeper sells salt at a rate of Rs 18 per kilogram. The MRP of the salt is Rs 15 per kg. As though not satisfied with this, he tries to multiply his profit by removing 200 gm from each packet. What is the shopkeeper’s gain percentage?

A) 15%                     B) 20%                   C) 25%                      D) 30%

Answer: The cost price of the salt is equal to Rs. 15/kg. However, the selling price is Rs. 18/kg. Thus the dealer makes a profit of Rs 3 per sale. In the terms of percentage, we can say that the rate of the profit or the profit percentage is equal to (3/15)×100 = 20%.

Now let us take into account his dishonesty. Since the dealer removes 200 gms from each kg or 100 gms, we can easily use the formula to find the actual profit that this dishonest dealer is generating. The formula says that Profit percentage or Gain percentage =  [(Error)/(True Value) – (Error)] × 100%. Substituting the values in this equation, we have:

Gain percentage = [(200)/(1000 – 200) gms]× 100% = 25%. Hence the shopkeeper’s new gain or profit percentage is 25% which is 5% more than what he would make if he is honest. Therefore the correct option is C) 25%.

Practice Question:

Q 1: There is a dishonest shopkeeper whose claim is that he sells a certain product at a cost of Rs 23/kg, which actually costs him Rs 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, a policeman finds that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. Does he gain or lose? If so how much?

A) 15%                     B) -15%                          C) 23.3%                    D) -23.3%

Ans: A) 15%

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