"Buy Half, Get Half KG Free!"

A seller has some quantity of rice with him. The seller offered his customer that if he/she buys half of the rice he has, he will give half kg of rice as a discount. The first customer accepts his offer and he purchased half of the rice and get half kg as extra. After selling the rice to the first customer he again makes the same offer for the second customer, and so on. The seller left with no quantity of rice after he made the fifth transaction.

The initial quantity of rice the seller had?

So the amount of rice that seller had... 

Amount of Rice The Seller Had

How he sold the rice?

We need to find the amount of the rice that seller had before each of the customer came for purchasing.

Since, no rice left after he made 5th transaction, he must had 1kg rice before this transaction. Half kg is purchased by 5th customer and half kg is given as a discount.

Before 4th customer, seller must had x kg where (x - x/2) - 1/2 = 1 i.e. x = 3 kg.

Before 3rd customer, seller must had y kg where (y - y/2) - 1/2 = 3 i.e. y = 7 kg.

Before 2nd customer, seller must had z kg where (z - z/2) - 1/2 = 7 i.e. y = 15 kg.

Before 1st customer, seller must had a kg where (a - a/2) - 1/2 = 15 i.e. y =31 kg.

Hence, the seller must had 31kg of rice initially. 

The Buyer Who is Thief

Once a man steals Rs.100 note from the shop. Later he purchases good of worth Rs.70 from the same shop using that note. The shopkeeper gives back Rs.30 in return. 

How much did shopkeeper loose in the case?


Do you think Rs.130? Or anything else? 

Loss Due To Thief Buyer

What's the case history? 

So did you just answer Rs.130 ? No, that's not correct!

Thief initially steals Rs.100 note. Now imagine instead of Rs.100 he steals goods of worth Rs. 70 + Rs.30 (given by shopkeeper). So eventually, the shopkeeper lost only Rs.100 in the process. 

In other words, the thief exchanges Rs.70 with the goods in the case. He pays for those goods to shopkeeper. So he looses Rs.70 from stolen Rs.100 & gains back via goods.

So eventually, the shopkeeper lost only Rs.100 in the case.

 

The Lossless Mistake

Bob buys two things in a shop. With his pocket calculator he calculates in advance what he has to pay: 5.25 dollars. But what he does not notice is that he pressed the division instead of the addition button. At the desk he is not surprised if he hears that he has to pay 5.25 dollars. 

What is the price of the two things Bob has bought?

Know the cost of those 2 things.

For Mistake To Be Lossless...

What was the mistake?

Let's assume that those things costs a and b respectively.

As per Bob's wrong calculation,

a / b = 5.25

a = 5.25 b  ..........(1)

And according to what should have been correct,

a + b = 5.25

Putting (1) in above,

5.25b + b  = 5.25

6.25b = 5.25

b = 0.84

Again putting this value in (1) gives,

a + 0.84 = 5.25

a = 5.25 - 0.84

a = 4.41

 
Hence the cost of 2 things are $4.41 and $0.84.

A Mathematical Buy!

In a classic wine shop in Flobecq, Belgium, list of three most popular wines are:

- The cost of 1 French wine bottle: 500$
- The cost of 1 German wine bottle: 100$
- The cost of 20 Dutch wine bottles: 100$

Homer Simpson entered the wine shop and he needs to buy

- All three types of wine shop.
- Needs to buy Dutch wine bottles in multiple of 20.
- Need to buy 100 wine bottles

Simpson has only 10000$. How many wine bottle(s) of each type, Simpson must buy? 

Simpson must buy.......Read More.... 

Source 
 

A Buy To Be Mathematical...

What was needed to buy?

Let's recollect the data where cost of each kind of wine bottle is listed.

- The cost of 1 French wine bottle: 500$
- The cost of 1 German wine bottle: 100$
- The cost of 20 Dutch wine bottles: 100$ (Cost of 1 bottle = 5$)

 

Now let F be the number of French bottle, G be the number of German bottles and D be the number of Dutch bottle that Simpson should buy.

F + G + D = 100

G = 100 - F - D   .....(1)

Total cost of all bottle must be $10000.

500F + 100G + 5D = 10000

Substituting (1) in above,

500F + 100(100 - F - D) + 5D = 10000

500F + 10000 - 100F - 100D + 5D = 10000

400F - 95D = 0

400F = 95D 
 
80F = 19D

D/F = 80/19

Possible values of D and F are 80 and 19 respectively.

From (1),

G = 100 - 19 - 80 =  1.

Let's verify if all these fits in his budget or not.  

19 French wine bottles would cost 19 x 500 = 9500, 1 German wine would cost = 1 x 100 = 100 and 80 Dutch wine bottles would cost 80 x 5 = 400. Remember we have got number of Dutch bottles in multiple of 20. Hence total cost = 9500 + 100 + 400 = 10000.

Hence with $10000, Simpson should buy 19 French, 1 German and 80 Dutch wine bottles if conditions of buying 100 bottles & Dutch bottles in multiple of 20 are applied.