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Commercial Arithmetic

Percentage

Percentage: The word 'per cent' means 'per hundred' or 'out of hundred'. Thus, we define 'percentage' as a fraction with 100 as its denominator. It is represented by the symbol '%'. Thus, = k per cent = k%.

To convert a percentage into a fraction: For converting a percentage into fraction, divide it by 100 and remove the symbol '%'. For example: .

To convert a fraction into percentage: For converting a fraction into percentage, multiply it by 100 and add the symbol '%'. For example: .

To convert a percentage into decimal: First convert the given percentage as a fraction and then convert this fraction into decimal form. Example: 53% = = 0.53.

To convert a decimal into a percentage: First convert the given decimal into a fraction and then multiply it by 100 to get the percentage. For example: 0.53 = = [ × 100]% = 53%.

Units
1 dozen = 12 units 1 score = 20 units 1 gross = 12 dozens
1 gross = 144 units 1 Hectare = 10000 sq.m 1 Are = 100 sq.m
100 Ares = 1 Hectare 1 decimetre = 10 cm 1 kilometre = 1000 m
1 metre = 100 cm 1 metre = 1000 mm 10 metres = 1 decametre
10 decimetres = 1 metre 1 kilometre = 100000 cm 1 inch = 2.54 cm
1 mile = 1.6 km approx. 1000 gms = 1 kg 1000 milligrams (mg) = 1 gram
100 kg = 1 Quintal 1000 kg = 1 metric ton 10 quintals = 1 metric ton
• Ex: What per cent of 40 is 48 ?
Sol:
Required percentage = (48/40) × 100 = (6/5) × 100 = 120%
• Ex: What per cent of 88 is 22 ?
Sol:
Required percentage = (22/88) × 100 = (1/4) × 100 = 25%
• Ex: What per cent of Rs. 2.50 is 40 paise ?
Sol: We know that 1 rupee = 100 paise. Thus, Rs. 2.50 = 2.50 × 100 = 250 paise.
 
Required percentage = (40/250) × 100 = (4/25) × 100 = 16%
• Ex: Find 60 % of 170.
Sol:
60 % of 170 = (60/100) × 170 = 6 × 17 = 102



What is percentile ?
Discount

Marked price: The price printed on an article or on a tag tied to it or the advertised price or the listed (catalogued) price is called the marked price, abbreviated as M.P. of the article.

Discount: In order to give a boost to the sale of an item or to clear the old stock, articles are sold at reduced prices. This reduction is given on the marked price of the article and is called discount. Simply, the reduction made on the marked price of an article is called discount.

Net price (or Selling price): The price of an article after deducting discount from the marked price is called the net price of the article.

Note: Discount is always reckoned on the marked price and normally offered as a percentage.

Important Formulae
The following formulae are generally used in solving the problems on discount.
• S.P. = M.P. – Discount.
• Discount = M.P. – S.P.
• Discount% = .
• If discount is d%, then S.P. = .
Ex: The M.P. of a ceiling fan is Rs. 950 and the shopkeeper allows a discount of Rs. 200 on it. Find its S.P.
Sol: Given that: M.P. = 950 and discount = 200. We know that: S.P. = M.P. – discount. Therefore,
S.P. = 950 – 200
= 750
∴ Selling price of a ceiling fan = Rs. 750.

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