The Discounted Purchases : Puzzle

Until last week, Mandy had been putting off the purchase of four major items for her home, waiting for her town's annual bargain days. Each year, the town's four main stores (including Nickels) each send out a coupon for a different percentage discount (10%, 15%, 20%, or 30%) on the purchase of a single item. Can you find the discount that Mandy received on each of her buys, and determine from which store she purchased each item?

Given:

Discounts      : 10%, 15%, 20%, 30%
Store Names : Stears, Pal-Mart, Nickels, Dullard's
Appliances    : Computer, Dishwasher, Lawnmower, VCR

Clues:

1) The percentage discount Mandy received on her new computer was twice that of the item she bought at Dullard's. 

2) The discount on the Stears purchase was ten percentage points lower than the one on the riding lawnmower. 

3) The discount on the dishwasher wasn't 15%. 

4) Pal-Mart, (which didn't issue the 30% off coupon) isn't the store at which Mandy purchased the VCR.

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The Discounted Purchases Puzzle : Solution

What was the challenge?

First let's have a given data.

Given:

Discounts: 10%, 15%, 20%, 30%
Store Names: Stears, Pal-Mart, Nickels, Dullard's
Appliances: Computer, Dishwasher, Lawnmower, VCR

Clues:

1) The percentage discount Mandy received on her new computer was twice that of the item she bought at Dullard's. 

2) The discount on the Stears purchase was ten percentage points lower than the one on the riding lawnmower. 

3) The discount on the dishwasher wasn't 15%. 

4) Pal-Mart, (which didn't issue the 30% off coupon) isn't the store at which Mandy purchased the VCR. 

 STEPS : 

1] As per clue (1), Dullard's didn't sell computer to Mandy and she didn't receive 10% or 15% off on computer. Also, Dullard's didn't offer her 20% or 30%.

2] The clue (2) suggests that the lawnmower wasn't purchased at 10% or 15% discount. Also, Stears discount must be 10% or 20%. And Stear didn't sell lawnmower for sure.

3] The clue (3) suggests that dishwasher wasn't sold at 15% discount. So, it's clear that Stears must have sold dishwasher at 10%/20% discount and Dullard's must have sold VCR at 15% discount. Therefore, computer must had been bought with 30% discount.

4] And hence, lawnmower at 20%. With that, Stears must have sold dishwasher at 10% discount as per clue (3).

5] Finally, as per clue (4), Pal-Mart didn't offer 30% discount suggests that it must not have sold computer. Therefore, Nickels sold computer at 30% discount and Pal-Mart sold lawnmower at 20% discount.

CONCLUSION : 

Final summary of the all purchases in form of table looks as - 

"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.