Discounts & Taxes

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“Discount is the reduction given on the Marked Price of an article to promote its sale.”

Marked Price

The original price marked for an item to be sold at. (MP)

Selling Price

The actual price an item is sold at. (SP)

Discount

\boxed{Discount = Marked\, Price - Selling\, Price}

\boxed{D= MP - SP}

Discount Percent

➣ Discounts are generally given as some percentage of the marked price on the item.
➣ In case of discounts, there is decrease in the selling price of the article. To get the discount percent we can use decrease percent formula, where Marked price would be our base.

\boxed{Discount \% = \frac{Discount}{MP} \times 100}

\boxed{Discount \% = \frac{(MP-SP)}{MP} \times 100}

Try These

1. A shop gives 20% discount. What would the sale price of each of these be?
(a) A dress marked at Rs 120.
(b) A pair of shoes marked at Rs 750.

2. A table marked at Rs 15,000 is available for Rs 14,400. Find the discount given and the discount per cent.

3. An almirah is sold at Rs 5,225 after allowing a discount of 5%. Find its marked price.

Solution

1. (a) Let SP be x
MP = Rs 120
Discount% = \frac{(MP-SP)}{MP} \times 100
\implies 20 = {\frac{(120-x)}{120} \times 10
⇒ 20×12 = (120-x)× 10
⇒ 2×12 = 120-x
⇒ 24 = 120−x
x = 120−24 = 96
∴ Sale Price of the dress = Rs 96.

(b) Let SP be x
MP = Rs 750
Discount% = \frac{(MP-SP)}{MP}\times 100
\implies 20 = \frac{(750-x)}{750} \times 100
⇒ 20×75 = (750-x)× 10
⇒ 2×75 = 750−x
⇒ 150 = 750−x
x = 750−150 = 600
∴ Sale Price of the Shoe = Rs 600

2. SP = 14400
MP = Rs 15000

Discount = MP − SP = Rs (15000−14400) = Rs 600
Discount% = \frac{(MP-SP)}{MP} \times 100
= \frac{600}{15000}\times 100
= 4\%

3. Let MP be x
SP = Rs 5225
Discount% = \frac{(MP-SP)}{MP} \times 100
\implies 5 = \frac{(x-5225)}{x} \times 100
\implies 5\times x = (x-5225)\times 100
\implies x-100x= - 522500
\implies -95x = -522500
\implies x =\frac {522500}{95}
\implies x = 5500
∴ Marked Price of the almirah = Rs 5500

Sales Tax / Value Added Tax

Sales tax is the extra money charged by the government to the customer on the sale of an item.
➢ It is collected by the shopkeeper from the customer and given to the government.
➣ It is always added on the selling price of an item to make the bill amount.
➣ It is added as some percentage of the selling price on the item.

Bill\, Amount = Selling\, Price + Sales\, Tax

Sales\, Tax = Bill\, Amount - Selling\, Price

\boxed{ST = BA - SP}

\boxed{ST \% =\frac{ST}{SP} \times 100}

\boxed{ST \% = \frac{(BA-SP)}{SP} \times 100}

Try These

1. Find the buying price of each of the following when 5% ST is added on the purchase of
(a) A towel at Rs 50
(b) Two bars of soap at Rs 35 each

2. If 8% VAT is included in the prices, find the original price of
(a) A TV bought for Rs 13,500
(b) A shampoo bottle bought for Rs 180

Solution

1. (a) Let BA be x
SP = Rs 50
ST% = \frac{(BA-SP)}{SP} \times 100
\implies 5 = \frac{(x-50)}{50} \times 100
\implies 5\times 5 = (x - 50)\times 10
\implies 25 = 10x - 500
\implies 10x = 525
\implies x = 52.5
∴ Buying Price of the towel = Rs 52.50

(b) Let BA be x
SP = Rs 35×2 = Rs 70
ST% = \frac{(BA-SP)}{SP} \times 100
\implies 5 = \frac{(x-70)}{70}\times 100
\implies 5\times 7 = (x-70)\times 10
\implies \frac{35}{10} = x-70
\implies 3.5 = x-70
\implies x = 70+3.5 = 73.5
∴ Buying Price of the soaps = Rs 73.50

2. (a) Let SP be x
BA = Rs 13500
VAT% = \frac{(BA-SP)}{SP} \times 100
\implies 8 = \frac{(13500-x)}{x}\times 100
\implies 8x = 1350000 \times 100x - 100x
\implies 108x = 1350000
\implies x= \frac{1350000}{108}
\implies x= 12500
∴ Original Price of the TV = Rs 12,500

(b) Let SP be x
BA = Rs 180
VAT% = \frac{(BA-SP)}{SP}\times 100
\implies 8 = \frac{(180-x)}{x} \times 100
\implies 8x <i>=</i> (180-x)\times 100
\implies 108x = 18000
\implies x = \frac{18000}{108}
\implies x = 166.67
∴ Original Price of shampoo bottle = Rs 166.67

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