RATIO & PROPORTION PART 1 BY: MAYANK AGNIHOTRI
RATIO Ratio is a relationship between two numbers indicating how many times the first number contains the second. Ratio of two quantities a and b in the same units, is the fraction and we write it as a: b Ex: A bag contain 5 red balls and 6 green balls then ratio of red balls to green balls is 5 6 and ratio of Red balls to total no. of balls is 5 11 In the Ratio a b, a is called first term or antecedent and b is called second term or consequent COMPOUNDED RATIO The compounded ratio of the ratios (a : b), (c : d), (e : f) is (ace: bdf). INVERSE RATIO If g is given ratio the 2 is its inverse ratio. (l DUPLICATE RATIO Duplicate ratio of (a : b) is (a2: b2)
SUB-DUPLICATE RATIO Sub-duplicate ratio of (a b) is (Va V) TRIPLICATE RATIO Triplicate ratio of (a: b) is ( a, b 3) SUB-TRIPLICATE RATIO Sub-triplicate ratio of (a : b) is (Va: Vb) COMPONENDO & DIVIDENDO If then atb ctd b d a-b c-d
PROPORTION The equality of two ratios is called Proportion If a b c: d, we write it as a:b::c:dand we say that a, b, c, d are in proportion. Here a and d are called extreme terms, while c and b are called mean terms. Product of means terms Product of extreme terms bx caxd EX 6 18::8:24 18 x 8 6 x 24144 144 Fourth Proportional If a b c: d, then d is called the fourth Proportional to a,b,c. Note: Three quantities of the same kind are said to be in continued proportion when the ratio of the first to the second is equal to the ratio of the second to the third. a, b, c are said to be in continued proportion if a b b:c Third Proportional : If a b b:c, then c is called the Third Proportional to a and b. Mean Proportional If a b b c, then b is the Mean Proportional between a and c.
QUESTIONS Ques 1. If a b 5:9& b:c- 4:7, find a:b:c. a 5b4 Sol make value of b same in both ratios a 5x4 b 4x9 a 20b 36 36 63 .. a b: c 20 36 63 An.s Ques 2. Find: I. Fourth proportional to 4, 9, 12; Il. Third proportional to 16, 36; Ill Mean Proportional between 2 & 8 Sol. 9x12 () 4:9 12:4xx9 x 12x227 Ans (II) 16 : 36 :: 36 :x#, 16xx-36x36-, X-361686-81 (11) Mean proportional between 2 & 8-V2 8-V16 = 4 Ans =_16_-81
Ques 3. Divide Rs 672 in the ratio 5: 3 Sol. sum of the ratios = 5 +3 = 8 First Part = 672 -= 420 Rs , Second part = 672 = 252 Rs 8 8 Ques 4. A mixture contains alcohol and water in the ratio 4:3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture. et the quantity of alcohol and water be 4x litres and 3x litres respectively. 20x = 4(3x + 5) So Then, 34+5 = 4 8x = 20 e x = 2.5 Quantity of alcohol (4 x 2.5) litres 10 litres.
B.Tech (ECE), Machine enthusiast, Inspired by an old hindi saying " Gyan baatne se badhta ha"