Logical Shopkeeper

Logic Level 3

A shopkeeper sells 3 chocolate bars for 1 rupee. Each chocolate bar has a wrapper. If you return 3 wrappers, you get an extra chocolate bar. How many chocolates at most can you get with 45 rupees?


The answer is 202.

Lakshya Singh by Lakshya Singh , 19, India

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2 solutions

Let S be the number of chocolate bars each rupee can buy.

S = 3 + 1 + 1 3 + 1 9 + ⋯ S = 3+1+\frac{1}{3}+\frac{1}{9}+\cdots 3 S = 9 + 3 + 1 + 1 3 + 1 9 + ⋯ = 9 + S 3S = 9+3+1+\frac{1}{3}+\frac{1}{9}+\cdots=9+S S = 9 2 S=\dfrac{9}{2}

Since the boy has 45 rupees, he can buy 202.5 chocolate bars. Since he cannot buy a fractional number of chocolate bars, we round it down to 202, which is the answer.

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Lakshya Singh
Jan 14, 2016

As we see we get 4 chocolates by paying 1 rupee. So the number of chocolates will be 180. But the extra chocolates would too account for the set of 3 chocolates. Out of 180 the number of extra chocolates are 45. Out of these 45, 15 chocolates are a set of 3 so we get 15 extra. Out of 15 , 5 are a set of 3 so 5 extra . Out of 5 ,1 is a set of 3 and 2 extra chocolates. But we get 1 extra chocolate from 3.So that would form one more set of 3 chocolates. So the total number of chocolates that we get in rupees 45 are: 180+15+5+1+1 = 202

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You don't get 4 chocolates per 1 rupees. You get 3. Either you entered question wrong or the answer.

Karan Sachdeva - 5 years, 5 months ago

I agree with Karan. We get 3 chocolates or 4 chocolates??????

Soumya Shrivastva - 5 years, 5 months ago

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We get 3 chocolates at first , but after returning the wrappers of the 3 chocolates we get one more chocolate. So effectively we get 3+1 equals 4 chocolates per rupee.

SURAJ BHAMBHANI - 5 years, 5 months ago

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Oh ya, thanks!!

Soumya Shrivastva - 5 years, 5 months ago

We're probably meant to assume that the boy returned the wrappers, so it would be 4.

Joseph Cristo Philip - 2 years, 2 months ago

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