Ratio And Proportion
In various competitive examinations, Quantitative Aptitude is one of the important subject and Ratio And Proportion plays a very vital part under this subject. If you want to appear for Bank PO, SSC, Railway, UPSC and other competitive examinations, then you must know Ratio And Proportion Concepts and Basics Formulas. We are providing sample questions of Ratio And Proportion Class 6, Ratio And Proportion Worksheet and Ratio And Proportion Sums for your easiness.
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Ratio And Proportion
Ratio And Proportion Concept
The ratio of two quantities a and b in the same units is the fraction and we write it as a: b.
In the ratio a: b, we call a as the first term or antecedent and b, the second term or consequent.
|Eg. The ratio 5 : 9 represents||5||With antecedent = 5, consequent = 9.|
Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.
Eg. 4: 5 = 8: 10 = 12: 15. Also, 4: 6 = 2: 3.
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Comparison of Ratios:
|We say that (a : b) > (c : d)||a||>||c||.|
The compounded ratio of the ratios: (a: b), (c: d), (e: f) is (ace: bdf)
Duplicate ratio of (a: b) is (a2: b2).
Sub-duplicate ratio of (a: b) is (a: b).
Triplicate ratio of (a : b) is (a3 : b3).
Sub-triplicate ratio of (a : b) is (a1/3 : b1/3).
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The equality of two ratios is called proportion.
If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion.
Here a and d are called extremes, while b and c are called mean terms.
Product of means = Product of extremes.
Thus, a : b :: c : d (b x c) = (a x d).
If a : b = c : d, then d is called the fourth proportional to a, b, c.
a : b = c : d, then c is called the third proportion to a and b.
Mean proportional between a and b is ab.
We say that x is directly proportional to y, if x = ky for some constant k and we write, x y.
We say that x is inversely proportional to y, if xy = k for some constant k and
|we write, x||1||.|
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Ratio And Proportion: Basic Formulas
Types of Ratio:
- Duplicate Ratio: This ratio is the square of two numbers. Example: 25:4 is the duplicate ratio of 5:2.
- Triplicate Ratio: This ratio is the cube of two numbers. Example: 125:8 is the triplicate ratio of 5:2.
- Sub-duplicate Ratio: This ratio is the square root of two numbers. Example: 5:2 is the sub-duplicate of 25:4
- Sub-triplicate Ratio: This ratio is the cube root of two numbers. Example: 5:2 is the sub-duplicate of 125:8
- Inverse Ratio: The ratio in which antecedent and consequent change their places. Example: 25:4 is the inverse of 4:25.
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Types of Proportions:
- Forth Proportion: When a:b = c:d, then d is called the forth proportion of a,b and c.
- Third Proportion: When a:b = b:c, then c is called the third proportion of a and b.
- Second Proportion: When a:b = b:c, then b is called second or mean proportion of a and c.
Ratio And Proportion Basics Shortcuts:
Ratio And Proportion Questions For Bank Po is given on below section of this page. To solve Ratio And Proportion Word Problems you have to apply one or more shortcuts which are presented below.
Shortcut 1: When A : B = m : n, and B : C = p : q. Then A : B : C = mp : pn :nq
Question 1: If A:B = 2:3 and B:C = 4:5, find A:B:C?
Solution 1: A:B:C = 2×4: 3×4: 3×5 = 8:12:15
Question 2: If A:B = 5:3 and B:C = 6:2, find A:B:C?
Solution 2: A:B:C = 30:18:6 (Try to solve this mentally. Its very easy)
Shortcut 2: When A : B = m : n, B : C = p : q, and C : D = r : s. Then A : B : C : D = mpr: npr : nqr : nqs
Question 1: If A:B = 2:3, B:C = 3:4, C:D = 4:5, find A:B:C:D?
Solution 1: 2x3x4: 3x3x4: 3x4x4: 3x4x5 = 24:36:48:60 (Try to solve this mentally)
Shortcut 3: In a container, the ratio between oil and water is P:Q. The total quantity is x litres. To find the amount of water to be mixed so that the ratio becomes A:B, use x(pb – qa) a(p + q)
Question 1: A container has oil and water in the ratio 2:3. The total quantity of oil and water is 10 liters. What amount of water should be added, so that the ratio becomes 1:3?
Solution 1: Solving by formula,
Amount of water to be added = 10 (2×3 – 3×1) = 10 (6-3) = 6 liters
1 (2+3) 5
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Ratio and Proportion Problems:
On the below section of this page we are presenting Ratio And Proportion Questions for your convenience. Candidates can also get Ratio and Proportion Worksheets, Ratio and Proportion Aptitude, etc on this page. So go through this page completely.
Ques1. Arrange the following ratios in descending order.
2 : 3, 3 : 4, 5 : 6, 1 : 5
Given ratios are 2/3, 3/4, 5/6, 1/5
The L.C.M. of 3, 4, 6, 5 is 2 × 2 × 3 × 5 = 60
Now, 2/3 = (2 × 20)/(3 × 20) = 40/60
3/4 = (3 × 15)/(4 × 15) = 45/60
5/6 = (5 × 10)/(6 × 10) = 50/60
1/5 = (1 × 12)/(5 × 12) = 12/60
Clearly, 50/60 > 45/60 > 40/60 > 12/60
Therefore, 5/6 > 3/4 > 2/3 > 1/5
So, 5 : 6 > 3 : 4 > 2 : 3 > 1 : 5
Ques2. Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers.
Sum of the terms of the ratio = 3 + 4 = 7
Sum of numbers = 63
Therefore, first number = 3/7 × 63 = 27
Second number = 4/7 × 63 = 36
Therefore, the two numbers are 27 and 36.
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Ques3. If x : y = 1 : 2, find the value of (2x + 3y) : (x + 4y)
x : y = 1 : 2 means x/y = 1/2
Now, (2x + 3y) : (x + 4y) = (2x + 3y)/(x + 4y) [Divide numerator and denominator by y.]
= [(2x + 3y)/y]/[(x + 4y)/2] = [2(x/y) + 3]/[(x/y) + 4], put x/y = 1/2
We get = [2 (1/2) + 3)/(1/2 + 4) = (1 + 3)/[(1 + 8)/2] = 4/(9/2) = 4/1 × 2/9 = 8/9
Therefore the value of (2x + 3y) : (x + 4y) = 8 : 9
Ques4. A bag contains $510 in the form of 50 p, 25 p and 20 p coins in the ratio 2 : 3 : 4. Find the number of coins of each type.
Let the number of 50 p, 25 p and 20 p coins be 2x, 3x and 4x.
Then 2x × 50/100 + 3x × 25/100 + 4x × 20/100 = 510
x/1 + 3x/4 + 4x/5 = 510
(20x + 15x + 16x)/20 = 510
⇒ 51x/20 = 510
x = (510 × 20)/51
x = 200
2x = 2 × 200 = 400
3x = 3 × 200 = 600
4x = 4 × 200 = 800.
Therefore, number of 50 p coins, 25 p coins and 20 p coins are 400, 600, 800 respectively.
Ques5. If 2A = 3B = 4C, find A : B : C
Let 2A = 3B = 4C = x
So, A = x/2 B = x/3 C = x/4
The L.C.M of 2, 3 and 4 is 12
Therefore, A : B : C = x/2 × 12 : x/3 × 12 : x/4 = 12
= 6x : 4x : 3x
= 6 : 4 : 3
Therefore, A : B : C = 6 : 4 : 3
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Ques6. What must be added to each term of the ratio 2 : 3, so that it may become equal to 4 : 5?
Let the number to be added be x, then (2 + x) : (3 + x) = 4 : 5
⇒ (2 + x)/(5 + x) = 4/5
5(2 + x) = 4(3 + x)
10 + 5x = 12 + 4x
5x – 4x = 12 – 10
x = 2
Ques7. The length of the ribbon was originally 30 cm. It was reduced in the ratio 5 : 3. What is its length now?
Length of ribbon originally = 30 cm
Let the original length be 5x and reduced length be 3x.
But 5x = 30 cm
x = 30/5 cm = 6 cm
Therefore, reduced length = 3 cm
= 3 × 6 cm = 18 cm
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Ques8. Mother divided the money among Ron, Sam and Maria in the ratio 2 : 3 : 5. If Maria got $150, find the total amount and the money received by Ron and Sam.
Let the money received by Ron, Sam and Maria be 2x, 3x, 5x respectively.
Given that Maria has got $ 150.
Therefore, 5x = 150
or, x = 150/5
or, x = 30
So, Ron got = 2x
= $ 2 × 30 = $60
Sam got = 3x
= 3 × 60 = $90
Therefore, the total amount $(60 + 90 + 150) = $300
Ques9. Divide $370 into three parts such that second part is 1/4 of the third part and the ratio between the first and the third part is 3 : 5. Find each part.
Let the first and the third parts be 3x and 5x.
Second part = 1/4 of third part.
= (1/4) × 5x
Therefore, 3x + (5x/4) + 5x = 370
(12x + 5x + 20x)/4 = 370
37x/4 = 370
x = (370 × 4)/37
x = 10 × 4
x = 40
Therefore, first part = 3x
= 3 × 40
Second part = 5x/4
= 5 × 40/4
Third part = 5x
= 5 × 40
= $ 200
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Ques10. The first, second and third terms of the proportion are 42, 36, 35. Find the fourth term.
Let the fourth term be x.
Thus 42, 36, 35, x are in proportion.
Product of extreme terms = 42 ×x
Product of mean terms = 36 X 35
Since, the numbers make up a proportion
Therefore, 42 × x = 36 × 35
or, x = (36 × 35)/42
or, x = 30
Therefore, the fourth term of the proportion is 30.
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