# Results The important thing in any kind of Age Problem, is to decide which age – present or past or future – to be taken as ‘x’!   Let us make a simple rule for ourselves – the ‘x’ should be the present age always.    In most cases, taking the present age as ‘x’, i.e., the base Geometry Lines and Angles Today, we are going to discuss a very interesting topic Simple and Compound interest. It deals with the money matters. By the end of it, we shall be familiar with the basic formulas used for the calculation of simple and compound interest and their practical applications. Various terms to be used along with their general representation are: Interest It is money paid by the borrower for using Concepts 1) There is a relationship between speed, distance and time: Speed = Distance / Time OR Distance = Speed* Time 2) Average Speed = 2xy / x+y where x km/hr is a speed for certain distance and y km/hr is a speed at for same distance covered. **** Remember that average speed is not just an average of two speeds i.e. x+y/2. It is equal to 2xy / x+y 3) Trick One simple technique is using days in denominator while solving questions. For example, A can do a job in 3 days and B can do the same job in 6 days. In how much time they can do the job together. Solution - 1/3 + 1/6 = 1/2, hence 2 days is the answer. Examiner can set the question in opposite way and can ask you how much The term percent means “for every hundred”. It can best be defined as- “A fraction whose denominator is 100 is called a percentage, and the numerator of the fraction is called the rate percent.   E.g. A man saves 10% of his monthly income means ‘A man saves Rs 10 out of every Rs 100 of his income. Some of the important prime fractions represented in percentage terms are given below- Time, Speed & Distance Important Formula Units conversion (1) units of Boats and streams Let us suppose (A) Speed of boat in still water = x kmph (B) Speed of stream = y kmph Then : Pipe and cistern concept Pipes and cisterns are almost the same as  time and work problems. There are two kinds of pipes. 1 Inlet pipe- it fills the tank. If a pipe fills a tank in x hours. Then in 1 hours, it will fill Problem on trains 1 Suppose there are two trains A and B having length a metre and running at a speed of x m/sec and y m/sec respectively. Here two cases arise- GEOMETRY To understand geometry there is three conceptual concept : Point, line and plane. Pointy: A circle which do not have radius is called point. But this type of circle is not possible. Therefore point does not have any ideal definition.           In other POLYGON Definition : A closed figure formed by three or more than side is called polygon. Important facts about polygon: 1 sum of all interior angle of ‘n’ sided polygon TRIANGLE Definition : A closed figure formed by three sides. Ø CONGRUENCY Congruent Figures :- Congruent means equal in all respects or figures whose shape and size are both the same. For example:- Two circles of same radii are congruent, also two squares of the same sides are congruent. Congruent Triangle Partnership  When two or more than two persons run a business jointly, they are called partners and the deal is known as partnership. 1. when investments of all the partners are for the same time the gain or loss is distributed among the partners in the ratio of their investments suppose A B- Brackets O-Orders (powers and roots) D-Division M-Multiplication A-Addition S-Subtraction Discount Marked price (= List price) : it is the price printed on the article. Discount = It is the commission given by the shopkeeper to the customer while selling that article. Discount= Marked price – selling price News = Make four directions, namely north, East, West, and South. Based on their combination, there are four more directions, namely, North-East, North-West, South-East and South-West. Profit & Loss! Tips & Tricks Important Concepts Cost Price Profit and loss Cost price : The cost at which an article is purchased is called its cost price (C.P.) Selling price : The price at which an article is sold is called its selling price (S.P.) Profit /Gain Mixture & Allegation (Notes) New Allegation is the rule that enables us :- (i) To find the mean or average value of mixture when the prices of two or more ingredients which may be mixed together and the proportion in which they are mixed are given (= Allegation Medial); and Average (Notes) New An average, or more accurately an arithmetic mean, is the sum of n different data divided by n. For example, if a batsman scores 41, 51 and 43 runs in first, second and third match respectively, then Average Related to speed (Notes-2) Theorem (1) : If a person travels a distance of a speed of x km/hr and the same distance at a speed of y km/hr, then the average speed during the whole journey is given by Height and Distance Angles of Elevation  and Depression : Suppose we are viewing an object. The line of sight or the line of vision is a straight line from our eye to the object we are viewing. * if the Trigonometry (Note-1) Pythogoras theorem : In a right- angled triangle, the square of hypotenuse is sum of the squares of the base and the perpendicular.