Comparing quantities: Comparing quantities Recall ratio and percentage: We know, ratio means comparing two quantities. A basket has two types of fruits, say,20 apples and 5 oranges. Then, the ratio of the number of oranges to the number of apples = 5 : 20 The comparison can be done using fractions as, 5 = 1 20 4
To study we have some examples: To study we have some examples Q: a picnic is being planed in a school for class 7 th . Girls are 60% of the total number of students and are 28 in number. The picnic site is 55km from the school and the transport company is charging at the rate of Rs 12 per km. The total cost of refreshments will be Rs 4280. Can you tell. 1:} The ratio of the number of girls to the number of boys of the class? 2:} The cost per head if two teachers are also going with the class? 3:} If their first stop is at a place 22Km from the school, what percent of the total distance of 55Km is this? What percent of the distance is left to be covered?
Solution 1: Solution 1 To find the ratio of girls and boys. Ashima and john come with the following answers. They needed to know the number of boys and also the total number of students. So, the number of boys = 30 – 18 =12 Hence the ratio of the number of girls to the number of boys is 18 : 12 or 18 = 3 is written as 3:2 and read as 3 12 2 is to 2.
PowerPoint Presentation: 2:} To find the cost per person. Transporting charge = distance both ways X rate = Rs {55 X 2} X 12 = Rs 110 X 12 = Rs 1320 total expenses = Refreshment charge + transporting charge = Rs 4280 + Rs 1320 = Rs 5600 total number of persons = 18girls +12boys +2 teacher = 32 persons Ashima and john then used unitary method to find the cost per head. For 32 persons, amount spend would be Rs 5600 The amount spend for 1 persons = Rs 5600 = Rs 175 32
PowerPoint Presentation: The distance of the place where the first stop was made = 22 Km. To find the percentage of distance: 22 = 22 X 100 = 40% 55 100 Out of 55 km, 22km are traveled Out of one km, 22 km are traveled 55
Discount percentage: Discount percentage A ratio is an expression that compares quantities relative to each other. When we compare two quantities in relation to each other, such a comparison is mathematically expressed as a ratio. Percent means ‘per hundred’ or out of hundred. Percentage is another way of comparing ratios that compares to hundred. A change in a quantity can be positive, which means an increase, or negative, which means a decrease. Such a change can be measured by an increase percent or a decrease percent. Percentage Change (Increase/Decrease)
PowerPoint Presentation: A discount is a price reduction offered on the marked price. Discounts are offered by shopkeepers to attract customers to buy goods and thereby increase sales. Discount = Marked price (MP) – Sale price (SP) A discount is, in fact, a percentage decrease, because the amount of change or discount is compared with the initial price or marked price.
PowerPoint Presentation: Sales tax is charged by the government on the selling price of an item and is included in the bill amount. Sales tax has been replaced by a new tax called Value Added Tax (VAT). Normally, VAT is included in the price of items like groceries. Profit and loss depend on cost price and selling price. If cost price is less than selling price, there is a profit. Profit is calculated by subtracting cost price from selling price. Profit = SP – CP If cost price is greater than selling price, then there is a loss. Loss is calculated by subtracting selling price from cost price. Loss = CP – SP.
Simple and Compound Interest : Interest is the extra money that a bank gives you for saving or depositing your money with them. Similarly, when you borrow money, you pay interest. With Simple interest, the interest is calculated on the same amount of money in each time period, and, therefore, the interest t earned in each time period is the same. On the other hand, compound interest is calculated on the principal plus the interest for the previous period. The principal amount increases with every time period, as the interest payable is added to the principal. This means interest is not only earned on the principal, but also on the interest of the previous time periods. So we can say that the compound interest calculated is more than the simple interest on the same amount of money deposited. When interest is compounded, the total amount is calculated using the formula Simple and Compound Interest
PowerPoint Presentation: Interest is generally calculated on a yearly basis. Sometimes, it can be compounded more than once within a year. It can be compounded half yearly , which means twice a year, or quarterly, which means four times a year. The period for which interest is calculated is called the conversion period . At the end of the conversion period , the interest is added to the principal to get the new principal . The formula to calculate the new rate of interest with respect to the conversion period is