Ratio & Proportion
In this part, we discuss bout Ratio & Proportion, and their properties
- Ratio
- Comparison of Ratio
- Proportion
- Continuous Proportion
- Properties of Proportion
Ratio
A Ratio is comparison of two or more quantities, expressed in same unit, by division.
Types of Ratio
There are different types of Ratio. Compounded Ratio. Duplicate Ratio. Sub Duplicate Ratio. Triplicate Ratio. Inverse Ratio or Reciprocal ratio.
Ratios - Problems
Ex. 1: The Ratio of the no. of Science students to the no. of arts students in a college of 1440 students is 3 : 5. If 36 new arts students are admitted in the college, find how many new Science students may be admitted so that the ratio of the no. of Science students to the no. of arts students may change to 2 : 3.
Ex. 2: The monthly earning of two women are in the ratio 4 : 5 and their monthly expenditures are in the ratio 7: 9. If each saves Rs.150 per month, find their monthly earnings.
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Ex. 3: The ratio of the prices of two flat was 16 : 25. Two years later when the price of the first has increased by 20% and that of the second by Rs.545, the ratio of the prices becomes 11 : 20. Find the original prices of the two houses.
Proportion
An equality of two or more ratios is called a proportion. For example, m, n, o, p are said to be in proportion if m: n = o : p (also written as m : n :: o: p)
Rules of Proportion
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Ex. Marks obtained by four students A, B, C & D are as follows :
A : B = 2 : 3, B : C = 4 : 5, C : D = 7 : 9, find the continued ratio A:B:C:D
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Ex. Find continued Ratio of 3/5: 4/7 : 5/8
Properties of Proportion
• Cross Multiplication : If a : b = c : d, then ad = bc
• Invertendo: If a : b = c : d, then b : a = d : c
• Alternendo : If a : b = c : d, then a : c = b : d
• Componendo : If a : b = c : d, then a + b : b = c + d : d
• Dividendo : If a : b = c : d, then a – b : b = c – d : d
• Componendo and Dividendo: If a : b = c : d, then a + b : a – b = c + d : c – d
• Addendo : If a:b=c:d, then a:b=c:d=(a+c):(b+d), or, a/b=c/d=(a+c)/(b+d)
• Subtrahendo : If a:b=c:d, then a:b=c:d=(a-c):(b-d), or, a/b=c/d=(a-c)/(b-d)
Proportions - Problems
Proportions - Problems
Ex. 1 : If (x/6) = (y/8) = (z/14), then prove that {(x+y+z) / z} =2
Ex. 2 : What should be added to the terms of 3 : 13 so to get 1 : 3.
Ex. 3 : What quantity must be added to each of the terms of the ratio a : b so that it may become equal to c : d ?
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Ex. 4 : An ornament weights 15 gm of which 5 gm is pure silver and the rest alloy. Find the ratio of pure silver to alloy?
Ex. 5: If a:b=c:d=5:3, what is the value of ad:bc & (a+c):(b+d)
Ex. 6: The ratio of annual incomes of A and B is 4 : 3 and their annual expenditure is 3 : 2 . If each of them saves Rs. 1000 a year, find their annual income.
Problem: The prime cost of an article was three times the value of material used. The cost of raw materials was increased in the ratio 3 : 4 and the productive wage was increased in the ratio 4 : 5. Find the present prime cost of an article, which could formerly be made for Rs. 180.
Summary
Ratio : Ratio a/b > c/d, if ad>bc, a/b = c/d, if ad=bc, Ratio a/b < c/d if ad<bc
Proportion - Rules : 1. If a : b = c : d, then ad = bc. 2.If a : b = c : d, then b : a = d : c
3. If a : b = c : d, then a : c = b : d 4. If a : b = c : d, then a + b : b = c + d : d
5. If a : b = c : d, then a – b : b = c – d : d 5. If a : b = c : d, then a + b : a – b = c + d : c – d
6. If a:b=c:d, then a:b=c:d=(a+c):(b+d), or, a/b=c/d=(a+c)/(b+d)
7. If a:b=c:d, then a:b=c:d=(a-c):(b-d), or, a/b=c/d=(a-c)/(b-d).
Videos
Click on the following link to play YouTube videos of the topics discussed in this chapter.
Videos
Click on the following link to play YouTube videos of the topics discussed in this chapter.