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A quantity A is said to vary inversely as another quantity B if the two quantities depend upon each other in such a manner that if B is increased in a certain ratio, A gets decreased in the same ratio and if B is decreased in a certain ratio, then A gets increased in the same ratio. What is this relationship called?
A quantity A is said to vary inversely as another quantity B if the two quantities depend upon each other in such a manner that if B is increased in a certain ratio, A gets decreased in the same ratio and if B is decreased in a certain ratio, then A gets increased in the same ratio. What is this relationship called?
Inverse variation
If there are three quantities A, B and C such that A varies with B when C is constant and varies with C when B is constant, then A is said to vary jointly with B and C when both B and C are varying. What is this relationship called?
If there are three quantities A, B and C such that A varies with B when C is constant and varies with C when B is constant, then A is said to vary jointly with B and C when both B and C are varying. What is this relationship called?
Joint variation
What is the formula for inverse variation?
What is the formula for inverse variation?
X₁Y₁ = X₂Y₂ or X₁/X₂ = Y₂/Y₁
The sum of two numbers is 84. If the two numbers are in the ratio 4:3, then find the two numbers.
The sum of two numbers is 84. If the two numbers are in the ratio 4:3, then find the two numbers.
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If 4a=3b, then find (7a+9b):(4a+5b).
If 4a=3b, then find (7a+9b):(4a+5b).
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The number of red balls and green balls in a bag are in the ratio 16:7. If there are 45 more red balls than green balls, find the number of green balls in the bag.
The number of red balls and green balls in a bag are in the ratio 16:7. If there are 45 more red balls than green balls, find the number of green balls in the bag.
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What least number must be added to each of a pair of numbers that are in the ratio 7:16 so that the ratio between the terms becomes 13:22?
What least number must be added to each of a pair of numbers that are in the ratio 7:16 so that the ratio between the terms becomes 13:22?
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A number is divided into four parts such that 4 times the first part, 3 times the second part, 6 times the third part, and 8 times the fourth part are all equal. In what ratio is the number divided?
A number is divided into four parts such that 4 times the first part, 3 times the second part, 6 times the third part, and 8 times the fourth part are all equal. In what ratio is the number divided?
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If x: y = 4:3, y: z = 2 : 3, find x: y: z.
If x: y = 4:3, y: z = 2 : 3, find x: y: z.
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If a/b = 4/5, then find (2a² + 3b) : (7a+6b²).
If a/b = 4/5, then find (2a² + 3b) : (7a+6b²).
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Two numbers are in the ratio 4:5. If 7 is added to each, the ratio between the numbers becomes 5:6. Find the numbers.
Two numbers are in the ratio 4:5. If 7 is added to each, the ratio between the numbers becomes 5:6. Find the numbers.
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The scores of Mohan and Sohan in a test are in the ratio 5:4. If their total score is 135, find Mohan's score.
The scores of Mohan and Sohan in a test are in the ratio 5:4. If their total score is 135, find Mohan's score.
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If a: b = 3:4, find 3a+4b: 4a+5b.
If a: b = 3:4, find 3a+4b: 4a+5b.
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The ratio of the number of marbles with Ram and Shyam is 19:13. If Ram gives Shyam 30 marbles, both will have equal numbers of marbles. Find the number of marbles with Ram.
The ratio of the number of marbles with Ram and Shyam is 19:13. If Ram gives Shyam 30 marbles, both will have equal numbers of marbles. Find the number of marbles with Ram.
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Two numbers are in the ratio 3:4. What part of the larger number must be added to each number so that their ratio becomes 5:6?
Two numbers are in the ratio 3:4. What part of the larger number must be added to each number so that their ratio becomes 5:6?
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1400 is divided into four parts such that twice the first part, thrice the second part, 4 times the third part and 12 times the last part are all equal. Find the 4 parts.
1400 is divided into four parts such that twice the first part, thrice the second part, 4 times the third part and 12 times the last part are all equal. Find the 4 parts.
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The curved surface area of a cylinder jointly varies directly with the height and the radius. When the height of the cylinder is 36 cm and the radius of the cylinder is 10 cm, the curved surface area of the cylinder is 720π cm². Find the curved surface area of the cylinder when the height of the cylinder is 54 cm and the radius of the cylinder is 15 cm.
The curved surface area of a cylinder jointly varies directly with the height and the radius. When the height of the cylinder is 36 cm and the radius of the cylinder is 10 cm, the curved surface area of the cylinder is 720π cm². Find the curved surface area of the cylinder when the height of the cylinder is 54 cm and the radius of the cylinder is 15 cm.
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Given that x varies directly as y, verify whether (x + y)³ varies directly with (x - y)³.
Given that x varies directly as y, verify whether (x + y)³ varies directly with (x - y)³.
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Study Notes
Ratio, Proportion, and Variation
- Key concepts in mathematics focusing on relationships between quantities.
- Ratio: A comparison of two quantities using division. Expressed as a:b or a/b.
- Proportion: A statement that two ratios are equal. Expressed as a:b = c:d or a/b = c/d.
- Direct Variation: When two quantities increase or decrease in the same proportion. Expressed as y = kx, where k is the constant of variation.
- Inverse Variation: When one quantity increases while the other decreases in the same proportion. Expressed as y = k/x, where k is the constant of variation.
- Joint Variation: When one quantity varies directly with the product of two or more other quantities. Expressed as z = kxy, where k is the constant of variation.
Solved Examples
- Illustrative problems demonstrating application of ratios, proportions, and various types of variation.
- Include examples involving numbers, quantities, and practical scenarios.
- Highlight mathematical reasoning and problem-solving techniques for application.
- Demonstrates the usage of formulas to solve variation problems.
- Clearly show the steps involved in calculating unknown parameters.
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Description
Explore the fundamental concepts of ratio, proportion, and variation in mathematics through this quiz. Understand how to express relationships between quantities and solve illustrative problems that demonstrate their application. Test your knowledge on direct, inverse, and joint variations with practical examples.
