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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
= Marked Price - Selling Price= MP − SP
➣ 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.
Discount % = Discount/MP × 100
Discount % = (MP−SP)/MP × 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 xMP = Rs 120
Discount% = (MP-SP)/MP × 100
⇒ 20 = (120-x)/12
⇒ 20×12 = (120-x)× 10
⇒ (20×12)/10 = 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% = (MP-SP)/MP × 100
⇒ 20 = (750-x)/75
⇒ 20×75 = (750-x)× 10
⇒ (20×75)/10 = 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% = (MP−SP)/MP × 100
= 60
= 4 %
3. Let MP be x
SP = Rs 5225Discount% = (MP-SP)/MP × 100
⇒ 5 = (x-5225)/x × 100
⇒ 5×x = (x - 5225)× 100
⇒ x = (x - 5225)× 100/5
⇒ x = 20(x- 5225)
⇒ x = 20×x−20×5225
⇒ 19x = 20×5225
⇒ x = 20×5225/19
⇒ x = 20×275 = 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
ST = BA − SP
ST % = ST/SP × 100
ST% = (BA−SP)/SP × 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 xSP = Rs 50
ST% = (BA-SP)/SP × 100
⇒ 5 = (x-50)/5
⇒ 5×5 = (x-50)× 10
⇒ 25/10 = x-50
⇒ 2.5 = x-50
⇒ x = 50+2.5 = 52.5
∴ Buying Price of the towel = Rs 52.50
(b) Let BA be x
SP = Rs 35×2 = Rs 70
ST% = (BA-SP)/SP × 100
⇒ 5 = (x-70)/7
⇒ 5×7 = (x-70)× 10
⇒ 35/10 = x-70
⇒ 3.5 = x-70
⇒ x = 70+3.5 = 73.5
∴ Buying Price of the soaps = Rs 73.50
2. (a) Let SP be x
BA = Rs 13500
VAT% = (BA-SP)/SP × 100
⇒ 8 = (13500-x)/x × 100
⇒ 8×x = (13500-x)× 100
⇒ x = (13500-x)× 100/8
⇒ x = 12.5(13500-x)
⇒ x = 12.5×13500−12.5×x
⇒ 13.5x = 12.5×13500
⇒ x = 12.5×13500/13.5
⇒ x = 12.5×1000 = 12500
∴ Original Price of the TV = Rs 12500
(b) Let SP be x
BA = Rs 180
VAT% = (BA-SP)/SP × 100
⇒ 8 = (180-x)/x × 100
⇒ 8×x = (180-x)× 100
⇒ x = (180-x)× 100/8
⇒ x = 12.5(180-x)
⇒ x = 12.5×180 −12.5×x
⇒ 13.5x = 12.5×180
⇒ x = 12.5×180/13.5
⇒ x = 12.5×13.3 = 166.67
∴ Original Price of shampoo bottle = Rs 166.67
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