Rpv session 1

Rpv session 1

• 1.
  CAT Concept Session 1:Ratio, Proportion and Variation www.georgeprep.com 9985-372-371
• 2.
  Session 1 Ratio –Introduction and Terminology Ratio - Properties Combining ratios Proportion – Properties Session 2 Variation – Properties Comparison of fractions – Part 1 Comparison of fractions – Part 2 Problem Set – 1 Problem Set -2 www.georgeprep.com 9985-372-371 Ratio, Proportion and variation
• 3.
  Ratio, Proportion andVariation – Session 1 • Ratio – Introduction and Terminology www.georgeprep.com 9985-372-371
• 4.
  Ratio – Whatis it?  Ratio: Comparison of magnitude of two quantities. www.georgeprep.com 9985-372-371 The ratio of the expenses of A and B is 5:9. If the sum of their expenses is Rs. 28000. - What is A’s expense? - By how much is B’s expense greater than A’s expense?
• 5.
  Ratio – Problemson basic understanding www.georgeprep.com 9985-372-371 What is the value of A:B:C ? If, a) A:B:C = 1 3 ∶ 1 2 ∶ 1 5 b) A 3 = B 2 = C 5
• 6.
  Ratio – Terminology Terminology  Antecedent and consequent  Let the ratio of A’s age and B’s age = a:b and B’s age and C’s age = b:c  Duplicate ratio of their ages =  Triplicate ratio of their ages =  Sub-duplicate ratio of their ages =  Sub-triplicate ratio of their ages = www.georgeprep.com 9985-372-371
• 7.
  Ratio – Terminology ⁻If 5a+2 : 12a+4 is the triplicate ratio of 3:4, what is the value of a? www.georgeprep.com 9985-372-371
• 8.
  Ratio, Proportion andVariation – Session 1 • Ratio – Properties www.georgeprep.com 9985-372-371
• 9.
  Ratio – Properties Propertiesof Ratios Value of ratios when multiplied or divided by the same number remains the same www.georgeprep.com 9985-372-371
• 10.
  Ratio – Properties Propertiesof Ratios Change of values of proper and improper fractions when the same value is added or subtracted to the Nr and the Dr. www.georgeprep.com 9985-372-371 Proper Fraction Improper Fraction
• 11.
  Ratio – Properties Propertiesof Ratios If 𝑎 𝑏 = 𝑐 𝑑 = 𝑒 𝑓 ……. then 𝑎 + 𝑐 + 𝑒 +⋯ 𝑏+𝑑+𝑓+⋯ = each of 𝑎 𝑏 , 𝑐 𝑑 … As long as (𝑏 + 𝑑 + 𝑓 + ⋯ ) ≠ 0 www.georgeprep.com 9985-372-371
• 12.
  Ratio – Properties Propertiesof Ratios • Given 𝑎 𝑏 , 𝑐 𝑑 , 𝑒 𝑓 , the value of 𝑎+𝑐+𝑒 𝑏+𝑑+𝑓 will be between the lowest and highest fraction. www.georgeprep.com 9985-372-371
• 13.
  Ratio – Properties Propertiesof Ratios - Summary • Value of ratios when multiplied or divided by the same number remains the same • Change of values of proper and improper fractions when the same value is added or subtracted to the Nr and the Dr. • If 𝑎 𝑏 = 𝑐 𝑑 = 𝑒 𝑓 ……. then 𝑎 + 𝑐 + 𝑒 +⋯ 𝑏+𝑑+𝑓+⋯ = each of 𝑎 𝑏 , 𝑐 𝑑 … As long as (𝑏 + 𝑑 + 𝑓 + ⋯ ) ≠ 0 • Given 𝑎 𝑏 , 𝑐 𝑑 , 𝑒 𝑓 , the value of 𝑎+𝑐+𝑒 𝑏+𝑑+𝑓 will be between the lowest and highest fraction. www.georgeprep.com 9985-372-371
• 14.
  Ratio – Properties www.georgeprep.com9985-372-371 If 𝑎+𝑏 𝑐 = 𝑏+𝑐 𝑎 = 𝑎+𝑐 𝑏 = p, what is the value of p? 1) 2 2) -1 3) -2 4) Either 1) or 2)
• 15.
  Ratio, Proportion andVariation – Session 1 • Combining Ratios www.georgeprep.com 9985-372-371
• 16.
  Ratio – Combiningratios www.georgeprep.com 9985-372-371
• 17.
  Ratio – Problems www.georgeprep.com9985-372-371 If A:B = 3:1, C:B = 2:1, C:D = 1:3 what is the value of A:D? 1) 1:2 2) 2:1 3) 1:3 4) None of these
• 18.
  Ratio – Problems www.georgeprep.com9985-372-371 A has thrice the amount of money that B has, B has twice the amount of money that C has and thrice the amount of money with C is equal to four times the amount of money with D. The amount of money with D is what percentage of the amount of money with A? 1) 200 2) 25 3) 12.5 4) None of these
• 19.
  Ratio, Proportion andVariation – Session 1 • Proportion – Properties www.georgeprep.com 9985-372-371
• 20.
  Proportion – Whatis it?  What is a proportion?  Product of extremes = product of means www.georgeprep.com 9985-372-371
• 21.
  Proportion – ContinuedProportion  If a:b =b:c, then a,b and c are in continued proportion. www.georgeprep.com 9985-372-371
• 22.
  Proportion – Properties Invertendo  Alternendo  Componendo  Dividendo  Componendo-dividendo www.georgeprep.com 9985-372-371
• 23.
  Proportion – Problems www.georgeprep.com9985-372-371 Ratio of p:q is the same as that of q:r, where p, q and r are positive numbers. If p = 16 and r = 100, find q. 1) 40 2) 64 3) 24 4) None of these
• 24.
  Proportion – Problems www.georgeprep.com9985-372-371 Find the fourth proportional to 1, 3 and 4 1) 12 2) 24 3) 18 4) None of these