Question

In what four ways can a shopkeeper cheat a consumer by using defective weights and measures ?

Answer 1

A dishonest dealer is one who claims to sell his product in welfare of customer but either he alters weight or he marks up price too high and then gives discount to attract customers.

Let us assume that the shopkeeper makes a gain of G% in selling his product.

Therefore,

(100+G)/(100+x) = True weight/ False weight

Here,

G = Overall gain percentage

X = %loss or % gain

Also, another formula that you can remember, in case the shopkeeper sells at the cost price, is:

Gain Percentage

profit-and-loss-Discounts-and-Marked-Price-2

Let us check this formula by taking an example.

Let us say that I went to a shop to by 1kg almonds. The shopkeeper told me that he is selling the almonds at the cost price but he actually used a faulty weight and gave me only 800gm. Let the cost which the shopkeeper paid for 1 kg was Rs 1000 and as he told me that he is selling at the cost price so I will pay him Rs 1000 for 1kg. But what I am getting instead 1kg, only 800gm. Now try to understand the logic. The shopkeeper sold me 800 gm almonds for Rs 1000 for which he actually paid Rs 800 (cost price of 800gm). So he gained 1000 – 800 = Rs 200 and his percentage profit = (200/800)x100

which is same as given above in the formula. Here 200 is the error and 800 = 1000 – 200 = True weight – Error.

So how to proceed with the problems when the shopkeeper is selling the articles at a price different from that of cost price while using faulty weight? In this case the shopkeeper will make two profits. First profit is because of the wrong weight and the second is because of the actual difference between the cost price and the selling price. The final profit percentage is arrived by using the result {P + Q + (PQ/100)} where P and Q are the two profits.

Let us understand it by a example.

Example : Let a dishonest shopkeeper sells sugar at Rs 18/kg which he has bought at Rs 15/kg and he is giving 800gm instead of 1000gm. Find his actual profit percentage.

Solution: Here the cost price of the sugar = Rs 15/kg

The selling price = Rs 18/kg.

The profit made by the shopkeeper is of Rs 3 and the profit percentage = 3/15 x 100 = 20%

This will be his total profit if he has actually sold 1 kg sugar. But that is not the case here as he is using the false weight.

Now the profit due to wrong weight =

profit-and-loss-Discounts-and-Marked-Price-2

= (200/800)x100 = 25%

The overall profit percentage = {P + Q + (PQ/100)} = [20+25+{(20 x 25)/100}] = 50%

You can also attempt this problem by another method.

The cost price of 1kg sugar is Rs 15. As the shopkeeper is giving only 800gm so the cost price of the 800 gm sugar is Rs 12. Here we have calculated the cost price of 800gm sugar because the shopkeeper is actually selling only 800gm. He is selling 800 gm sugar for Rs 18 for which he had paid Rs 12. So he gained Rs 6 and the profit percentage = 6/12 x 100 = 50%

The answer in this case is same as calculated above but the first method is more easy than the second one. Just find the individual profits and put the values in {P + Q + (PQ/100)}

The above formula is also valid if the shopkeeper is making losses due to some reason.