Hi Welcome to Quant Funda!! This is my first post and hence few words are required to explain the purpose of this post and subsequent ones.I have been teaching students Quant and DI for CAT exam , for quite some time now!! and I have observed students face a lot of difficulties in answering questions which involve using some basic concepts. In short the purpose of this post and all subsequent ones is to discuss the concepts related to CAT quant syllabus. The methodology will be to pick up a problem and discuss all facets of that problem. So here I go..
Faulty balance problem
A dishonest shopkeeper uses a false balance to defraud to the extent of 15% in buying sugar and also defrauds to the extent of 15% while selling the sugar. What percent does he gain on his outlay by doing this fraud.
This problem can be attempted in the following way.Since the shopkeeper is defrauding to the extent of 15% while buying that means whatever weight of sugar he is telling to the seller, i.e. the person from whom he is buying , he will tell 15% less. Let us say he gets 1kg of sugar that means the weight he tells to the seller must be 15% less i.e. 85% of 1kg. So he pays for only .85 kg. Now while selling he defrauds again to the same 15% , hence he will sell 1 kg as 15% more in weight. So he will sell 1 kg as 1.15kg .So total extra weight that he has gained will be .30 kg.But this .30kg weight of sugar he is getting by paying for .85 kg of sugar . hence his profit is (.30/.85)*100= (35+(5/17))%.
Till now it was simple ..
Let us have a look at another solution provided by a student(hereby referred to as S1) S1 says. Let the shopkeeper tell the seller that sugar that he is buying is 1kg. As he is defrauding to the extent of 15% , hence actual weight of sugar that he gets is 15% higher that is 1.15kg. this weight will be sold as 15% higher weight i.e. as 1.15*1.15 = 1.3225kg. hence he has gained .3225kg of sugar just by paying for 1kg of sugar , hence his gain will be (.3225/1)*100= 32.25%!!!! so which answer is correct the first one or the second one!!!!!!!!!!!!
Let us have a closer look at S1's argument. In the first solution the shopkeeper is reducing the actual weight that he is getting by 15% and in the second case he is increasing the reported weight by 15%. This is the error in student's solution. the shopkeeper is simply playing around with what he has !!! He tells less while buying of what he has got and tells more while selling it. So here the base is the amount that the shopkeeper has and not what he tells to buyer or seller.!!!! hence if he tells the seller that weight is 1 kg then actual weight will not be 1.15 kg but it will 1/.85 kg( let the actual weight that shopkeeper gets be "x" kg then reported weight will be 85% of this weight x , hence .85x =1 .Hence x= 1/.85 = 20/17kg). This weight will then be sold as 15% higher weight that is 1.15 times of 20/27 kg . This weight is = 20*1.15/17= 23/17. hence his gain will be 23/17 - 1 = 6/17 kg. This gain is made by paying for only 1 kg of sugar!! hence profit% = 6*100/17= (35+5/17)%!!!!which is same as the earlier solution . The error that has been made over here is this while buying the reported price has been made as the base and while selling the actual quantity available has been used as the base!!!
So we need to be consistent either use the fact that shopkeeper is defrauding on the amount that he is getting(during buying ) and on what he has (while selling) or on what he is reporting during buying and selling.
Let us work with other approach , i.e. he is defrauds on reported values. So if he tells the seller that weight is 1kg he is getting 15% higher of that i.e 1.15kg . Similarly while selling he will tell 1kg weight as 15 % lesser i.e. .85kg .Therefore if he actually has 1.15 kg the weight that he will report will be calculated as follows.Let the reported weight be x , then .85x =1.15kg Therefore x= 1.15/.85 =23/17kg. hence he gets paid for 23/17kg and pays for only 1kg , hence his profit is value of 6/17 kg of sugar , hence profit % is 6/17 *100 = (35+5/17)%!!
Hope this was useful!!! So keep reading more concpets are likely to follow!!!!
