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Arithmetic - Do What You Know

We have read a lot about one way of handling complex questions – simplify them to a question you know how to solve. Here is another way – first do what you do know, and then figure out the rest!


We know that basic concepts are twisted to make advanced questions. Our aim is to break down the question into two parts – ‘the basic concept’ and ‘the complexity’. You can either deal with the complexity first and then glide through the basic concept or you can glide through the basic concept first and then face the complexity. The method you use will depend on the question. If the question seems too complex at the outset, it means you will have to deal with the complexity first. If the question seems familiar but has some extra not-so-familiar elements, it means you should get the familiar out of the way first. Let’s take a question today to see how to do that.


Question: During a sale of 20% on everything in a store, a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies. The store still makes a profit of 12% on this sale. What is the mark up percentage on each candy?

(A) 100%
(B) 80%
(C) 75%
(D) 66+2/3%
(E) 55%



This question can get very messy if you let it! We have seen people working on this question with multiple variables: C for cost price, S for sale price, M for marked price etc. That can get very confusing because there are two types of mark up – the actual mark up (the store marks up the price of every candy by this percentage and lists it on the candy) and the effective mark up (because the kid takes 6 extra candies, this is the effective mark up). So let’s not go the algebra way.


Instead, let’s focus on what we can do without much effort. As a first step, let’s do what we know already (and hope that the rest will work out!).


We already know the relation between mark-up, discount and profit. The problem is that this question has another aspect – the kid takes 20 candies but pays the price of only 14 candies (which is the price obtained by reducing the marked price by 20% of discount). But let’s worry about it later.


Let’s first deal with the mark-up, discount and profit aspect of the question.


We know that (1 + m/100)(1 – d/100) = (1 + p/100) 


Since p is the effective profit that the store got, m must be the effective mark up here.

(1 + m/100)(1 – 20/100) = (1 + 12/100)

(1 + m/100) = (5/4)*(28/25)

(1 + m/100) = 7/5

m = 40


So effective mark up was 40% – i.e. 40% was the mark up in a situation where 14 articles were sold and charged for. This tells us this – effective mark up turned out to be 40% though his actual mark up must have been higher since he gave away 20 articles for the cost of 14.


Now what we already know is done. We get to the really tricky part – the thing that makes this question different – how do we find the actual mark up?


Let’s say the cost price of each of the 20 candies was $1. Then total cost price for the 20 candies was $20. This is the cost of the candies to the store. The effective markup was 40% i.e. the articles were effectively marked at 20 + (40/100)*20 = $28. The store gave a discount of 20% on this amount and made a profit of 12%. But this amount of $28 actually represents the mark up on 14 candies only. The cost price of 14 candies is $14 to the store. So the actual mark up percentage on the 14 candies is (28 – 14)/14 * 100 = 100%


Answer (A)


Obviously, there are many other ways of solving this question. See if you can figure out another one on your own!


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