# A problem from VAT:-A retailer buys an article at a discount of 15% on the printed price from a wholesaler. He marks up the price by 10%. Due to competition in the market, he allows a discount of...

A problem from VAT:-

A retailer buys an article at a discount of 15% on the printed price from a wholesaler. He marks up the price by 10%. Due to competition in the market, he allows a discount of 5% to a retailer. If the buyer pays Rs. 6771.60 for the article inclusive of 8% VAT, find :

1. the printed price of the article,

2. the profit percent of the article,

3. VAT paid by the retailer.

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The most important thing to remember here is that you have to be careful about the percentages. You can't just add them up and say that the price for the consumer was 10% off the original price.

First, find out how much the VAT was.

6771.6 = 1.08x because it equals the price plus 8% of the price for VAT.

x = 6270

So the seller got Rs 6270 and must have paid Rs 501.6 in VAT.

Now find the printed price.

The original discount was 15% so the retailer buys it for 85% of the printed price.

He marks it up 10%. This means he marks it up 10% of 85% -- not 10% of the original price. So now the price is 93.5% of the printed price.

From there, he allows a 5% discount (off of the 93.5%). Once you do the math here, the price to the customer is 89% of the printed price (actually .888 but I rounded up).

So Rs 6270 is actually 89% of the printed price.

6270 = .89x

So the printed price was Rs 7044.94

Now to find the profit.

How much did the retailier buy it for? He paid 85% of the printed price, or 85% of 7044.94. This is Rs 5988.2

So he got 6270 for the item and paid 5988.2. This means he got Rs 281.8 of profit.

281.8 is 4.7% of 5988.2

Let the original price be x.

After 15% discount, the retailer's purchase price is x*85% =0.85x. A markup by 10% on the 0.85x would be = 0.85x*110/100 = 0.935x. A discount of 5% on this value of 0.935x is 0.935x*95/100 = 0.88825x . Adding an 8% VAT on this would be : 0.88825*1.08 = 0.95931x. So this should be the price, Rs 6771.60 given by the buyer. So, the equation to get the original price x is:

0.95931x = Rs 6771.6 or

x= 6771.6/0.95931 = Rs 7058.82 is the original price.

After 15% discount he purchsed it for 7058.82 -15% (7058.82) = Rs 6000.

His marked up price = Rs6000+10%(6000) = 6600.

His sells for the amount(after 5% discount) = 6600-5%(6600) =Rs6270 + 8% of 6270 vat = Rs6270+Rs501.60 = Rs6771.60.

The printed price of the article while selling = Rs 6600.

Vat paid by the retailer = Rs501.6.

Profit of the retailer: Selling price (excluding vat) 6270 - purchase price Rs 6000 by the retailer = Rs 270.