TIME AND DISTANCE IMPORTANT FACTS AND FORMULAE 1. Speed = [Distance/ Time], Time=[Distance/Speed], Distance = (Speed* Time) 2. x km/hr = [x*5/18] m/sec. 3. If the ratio of the speeds of A and B is a:b, then the ratio of the times taken by them to cover the same distance is l/a : l/b or b:a. 4. x m/sec = [x* 18/5] km/hr. 5. Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. then, the average speed during the whole journey is [2xy/x+Y] km/hr. PROFIT AND LOSS IMPORTANT FACTS AND FORMULAE Cost Price : The price at which an article is purchased, is called its cost price, abbreviated as C.P. Selling Price : The price at which an article is purchased, is called its cost price, abbreviated as C.P. Profit or Gain : The price at which an article is purchased, is called its cost price, abbreviated as C.P. Loss : If S.Pis less than C.P., the seller is said to have incurred a loss. 1. Gain = (S.P.) - (C.P.) 2. Loss or gain is always reckoned on C.P. 3. gain% = [Gain*100/C.P.] 4. Loss = (C.P.) - (S.P.) 5. Loss% = [Loss* IOO/C.P.] 10. If an article is sold at a gain of say, 35%, then S P . . = 135% of C.P. 11. If an article is sold at a loss of say, 35%, then S P PROBLEMS ON TRAINS IMPORTANT FORMULAE 1. a km/hr = [a * 5/18]m/s. 2. a m/s = [a * 18/5] km/hr. 3. Time taken by a trian of length I metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover I metres. 4. Time taken by a train of length I metres to pass a stationary object of length b metres is the time taken by the train to cover (l + b) metres. 5. Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u>V, then their relatives speed = (u - v) m/s. 6. Suppose two trains or two bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s 7. If two trains of length a metres and b metres are moving in opposite directions at u 8. If two trains of length a metres and b metres are moving in the same direciton at u m/s and v m/s, then the time taken by the faster train to cross the slower train = (a + b)/(u - v) sec. 9. If tow trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then (A's speed) : (B's speed) = (11b : Va). TIME AND WORK IMPORTANT FACTS AND FORMULAE 1. 1 Work from Days: If A can do a piece of work in n days, then A's 1 day's work = n 1 Days from Work: If A's 1 day's work = then A can finish the work in n days. n' Ratio: If A is thrice as good a workman as B, then: Ratio of work done by A and B = 3 : 1. Ratio of times taken by A and B to finish a work = 1 : 3. PROBABILITY IMPORTANT FACTS AND FORMULAE 1. 2. 3. Experiment: An operation which can produce some well-defined outcomes is called an experiment. Random Experiment: An experiment in which all possible outcomes are know and the exact output cannot be predicted in advance, is called a random experiment. Examples: ii. Details: v. vi. vii. Rolling an unbiased dice. Tossing a fair coin. Drawing a card from a pack of well-shuffled cards. Picking up a ball of certain colour from a bag containing balls of different colours. When we throw a coin, then either a Head (H) or a Tail (T) appears. A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6 respectively. When we throw a die, the outcome is the number that appears on its upper face. A pack of cards has 52 cards. It has 13 cards of each suit, name Spades, Clubs, Hearts and Diamonds. Cards of spades and clubs are black cards. Cards of hearts and diamonds are red cards.
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