Lets start with the first and basic topic RATIO & PROPORTION. BASIC CONCEPTS OF RATIO AT A GLANCE 1) RATIO: A ratio is a relationship between two quantities of same kind, i.e in same unit by fraction. The ratio of a to b is written as a : b = a / b . In this, Numerator a is called as first term or ANTECEDENT , & Denominator b is called as second term or CONSEQUENT. 2) Ratio is UNIT FREE, i.e it has NO UNIT. 3) If a > b, then a : b is a ratio of GREATER INEQUALITY. If b > a, then a : b is a ratio of LESS INEQUALITY. If a = b, then a : b is a ratio of EQUALITY. 4) Usually a ratio is expressed in lowest term or in its simplest form. 5) Rule: The multiplication or division of each term of a ratio by the same non -zero number does not affect the ratio, i.e it remains UNCHANGED. 6) i) DUPLICATE RATIO - A ratio compounded to itself is called its duplicate ratio. Thus Duplicate ratio of a : b is a² : b² . ii) TRIPLICATE RATIO of a :b is a³ : b³ iii) SUB-DUPLICATE RATIO of a : b is √a :√b iv) SUB-TRIPLICATE RATIO of a : b is ³√a :³√b v) INVERSE OR RECIPROCAL RATIO of a : b is b : a EXERCISE Q1) In the word BALLOONS, the ratio of vowels to consonants is A. 3 : 5 B. 3 to 8 C. 5:3 D. 8/ 5 Q2) If a:b = 2:3 and b:c = 4:3, then a:b:c is A. 8:12:9 B. 2:3:8 C. 2:3:9 D. 2:3:12 Q3) If the length & breadth of a room measure 14 feet 3 inches and 11 feet 6 inches respectively, then the ratio of length & breadth is A. 18 : 56 B. 57 : 46 C. 56 : 22 D. 57 : 36 Q4) The ages of A and B are in the ratio 3 : 1. Fifteen years hence, the ratio will be 2 : 1. Their present ages are : A. 30 years, 10 years B. 45 years, 15 years C.21 years, 7 years D.60 years, 20 years Q5) The ratio of the incomes of A and B is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs. 1600, then the income of A is : A.Rs. 3400 B.Rs. 3600 C.Rs. 4000 D.Rs. 4400 Q6) If P : Q is the sub duplicate ratio of P-X² : Q-X², then X² is A. P / P + Q B. PQ / P-Q C. PQ / P+ Q D. None of the above Q7) If a : b = 3 : 5, b: c = 2 : 3 and d is 50% more then e, then the ratio between a and e is A. 2 : 3 B. 3 : 4 C. 3: 5 D. 4 : 5 PRACTICE THESE QUESTIONS AND U CAN COMMENT/ MESSAGE ME FOR ANSWERS, DOUBTS, ETC. DO SHARE THIS.
Posted on: Fri, 19 Sep 2014 16:32:07 +0000
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