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• Subgroups

Let be a group and any subset of . Let be any two elements of . Now being members of the product of surely belongs to , but it may or may not belongs to . If, however, belongs to , we say that is stable for the composition in and the composition in has […]

• Profit and Loss

For the purpose of comparison, we usually express the actual profits or loss as a percentage of cost price. For example, a shopkeeper sold an article for Rs.60 which costs Rs.50 and another article sold for Rs.110 which cost Rs.100. In each case, shopkeeper makes a profit of Rs.10. It seems that in both cases […]

• Concept of Discount

It is usually seen that the retailers cannot sell defective items, old items, etc. at the retail-selling price. If these items are sold at lower price, then it is called sale price. The difference between marked price (selling price) and the sale price, is called discount. In other words, a reduction in the price of […]

• Concept of Commission

A commission is the payment, an agent gets for selling or buying something on behalf of another person. It is usually written as a percentage of cost price or selling price. Example: An agent got 2% commission on selling a plot for 1000000. Find his commission. Solution: Let       Sale Price = 1000000 Commission Rate […]

• Concept of Rate

Before defining rate, first we consider some examples. 1. If one dozen eggs cost 24 Rs., what is the cost of 1 egg? (Ans). One dozen eggs cost = 24 Rs             Cost of 1 egg = 24/12=2Rs/egg 2. A car travels 540 km consumed 60 liters petrol. Find distance travelled in liter. (Ans). In […]

• Concept of Percentages

Comparison of fractions is not an easy task, especially when the two fractions have different denominators. For example; if you are asked which of the fractions and is greater than the other. i.e. we want to compare, whether  is greater than or less than . Since, denominators of  and are different. To compare these fraction, […]

• Expressing One Quantity as Percentage of Another Number

In a school, 56 out of 70 teachers are female. What percentage of the teachers are females? What percentage of them is male? The fraction of female teachers in the school is 56/70 changing this fraction to percentage we have x 100% = 80% 80% of the teachers are female and percentage of male teachers […]

• Percentage Changing

The change in the value of an item can be expressed as a percentage increase or decrease of the original value. An increase of 5% in the salary of a men who earns Rs.500 per month. That means, there is an increase of Rs.5 For every hundred (100). i.e. after increase, Rs.100 becomes 105. Therefore, […]

• Concept of Ratio

Sometimes, we have to deal with the quantities whose comparison is required. Suppose in a class of 45-students, 15 of the students are girls, 30 of the students are boys, and then we can compare the number of boys with number of girls in two different ways. 1. There are 15 more boys than girls […]

• Uses of Ratio and Continued Ratio

Ratio is used for calculating continued ratio, proportion, rates, percentage as well as continued proportion. Ratio can also be used for dividing the profit or amount between two or more people. For this we have the following process: First, we find sum of given ratios. Share can be divided by the following formula. Share of […]

• Continued Proportion

Quantities are said to be in continued proportion if the first is related to the second, the second is related to the third and the third is related to the forth and so on. If are in continued proportion then Example: Three persons A, B and C earned a profit of 70000 Rs in a […]

• Examples Uses of Ratio and Continued Ratio

Example: A profit of Rs. 8920 is to be divided among four persons in the ratios 5 : 9 : 11 : 15 respectively. How much does partner get? Solution: Given Profit = 8920 Ratio between Share = 5 : 9 : 11 : 15 Sum of ratios = 5 + 9 + 11 + […]