Mathematics Proportions and Ratios Quiz
48 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the weight of the nitrogen compound in 20 kg of fertilizer?

  • 3 kg
  • 3.6 kg (correct)
  • 2 kg
  • 4 kg

    • The weight of the potassium compound is 3.6 kg.

    False

    How much petrol does the car consume to cover 200 km?

    20 litres

    The bullock-cart takes __________ hours to cover a distance of 100 km at the speed of 5 km/hr.

    <p>20</p> Signup and view all the answers

    Match the following quantities with their types of proportion:

    <p>Nitrogen compound weight in fertilizer = Direct proportion Speed and time of the Car = Inverse proportion Distance covered per litre of petrol = Direct proportion Speed and time of the Bullock-cart = Inverse proportion</p> Signup and view all the answers

    Which of the following statements best describes direct variation?

    <p>As one quantity increases, the other also increases proportionally.</p> Signup and view all the answers

    The ratio of speed and time for the bullock-cart is a direct variation.

    <p>False</p> Signup and view all the answers

    In a direct variation, the product of two quantities is __________.

    <p>constant</p> Signup and view all the answers

    What method uses the equation $\frac{a}{b} = k$ to relate variables?

    <p>Invertendo</p> Signup and view all the answers

    The Componendo method states that if $\frac{a}{b} = \frac{c}{d}$ then $a + b = c + d$.

    <p>False</p> Signup and view all the answers

    If $ba = 74$, what is the next step to find the ratio $5ab - b$?

    <p>Substitute $a$ from $a = \frac{74}{b}$ and then calculate $5(\frac{74}{b})b - b$.</p> Signup and view all the answers

    The method that relates $\frac{ba}{dc}$ to $\frac{a+b}{c+d}$ is called __________.

    <p>Componendo</p> Signup and view all the answers

    Match the following methods with their definitions:

    <p>Invertendo = Switches numerator and denominator Componendo = Combines numerators and denominators Alternando = Expresses variable ratios in a different form Dividendo = Relates to dividing terms</p> Signup and view all the answers

    If $\frac{b}{d} = 3$, which of the following indicates the relationship between $a$ and $b$ using the Alternando method?

    <p>$a = \frac{b}{3}$</p> Signup and view all the answers

    The relationship $\frac{a+c}{b+d}$ holds true in all cases of the Componendo method.

    <p>False</p> Signup and view all the answers

    Using the Componendo-Dividendo method, if $ba = dc$, express $\frac{a-b}{c-d}$.

    <p>The ratio is $\frac{a - b}{c - d} = \frac{b(c-d)}{d(a-b)}$.</p> Signup and view all the answers

    What are the values of x and y that solve the equations x + y = 14 and x - y = 2?

    <p>(8, 6)</p> Signup and view all the answers

    The general form of a linear equation in two variables is ax + by + c = 0, where both a and b can be zero.

    <p>False</p> Signup and view all the answers

    If the sum of the ages of the mother and son is 45 years, and the mother's age is x, what is the son's age in terms of x?

    <p>45 - x</p> Signup and view all the answers

    The simultaneous equations can be solved by eliminating one of the __________.

    <p>variables</p> Signup and view all the answers

    Match the following equations with their respective solutions:

    <p>x + y = 14 = (8, 6) x - y = 2 = (8, 6) 2x + 3y = 1 = (−1, 1) 3x - 4y - 15 = 0 = (5, 0)</p> Signup and view all the answers

    What is the age of the son if the mother's age is 33?

    <p>12</p> Signup and view all the answers

    The equation 3x + y - 5 = 0 is in the standard form of a linear equation.

    <p>True</p> Signup and view all the answers

    What is the final value of y when solving the equations x + y = 45 and 2x - y = 54?

    <p>12</p> Signup and view all the answers

    What is the value of x in the equation 3x = 16 + 4y when y = 2?

    <p>8</p> Signup and view all the answers

    The solution to the equation 3x - 4y = 16 is (8, 2).

    <p>True</p> Signup and view all the answers

    What is the value of y when x is 1 in the equation y = 3x - 2?

    <p>1</p> Signup and view all the answers

    The coordinates of the solution of the given equations are (__, __).

    <p>(8, 2)</p> Signup and view all the answers

    Match the equations with their corresponding transformations:

    <p>3x = 16 + 4y = y = 3x - 2 3x - y = 2 = 17x - 6 = 11 2x - 3y = 10 = 3x - 4y = 16 8x + 3y = 11 = x = 8</p> Signup and view all the answers

    What do you get when you solve the equation 2(16 + 4y)/3 - 3y = 10?

    <p>y = 2</p> Signup and view all the answers

    The equation 8x + 9x - 6 = 11 simplifies to x = 7.

    <p>False</p> Signup and view all the answers

    Write one solution of the equation x + y = 7.

    <p>(3, 4)</p> Signup and view all the answers

    What is the total planned expenditure for Mr. Shah?

    <p>Rs. 1,58,000</p> Signup and view all the answers

    Mr. Shah has Rs. 4,82,000 available for yearly expenses after planned expenditures.

    <p>True</p> Signup and view all the answers

    How much interest did Mr. Shah earn from his bank investment?

    <p>Rs. 67,200</p> Signup and view all the answers

    Mr. Shah invested Rs. _________ in mutual funds.

    <p>2,40,000</p> Signup and view all the answers

    Match the following investments to their outcomes:

    <p>Bank Investment = Rs. 67,200 interest Mutual Funds = Rs. 3,05,000 after 2 years Insurance Premium = Rs. 24,000 annually Provident Fund Contribution = Rs. 1,28,000 annually</p> Signup and view all the answers

    Which of Mr. Shah's investments yielded a higher profit?

    <p>Mutual Funds</p> Signup and view all the answers

    Mr. Shah's total annual income is less than Rs. 6,40,000.

    <p>False</p> Signup and view all the answers

    What formula is used to calculate compound interest?

    <p>I = A - P</p> Signup and view all the answers

    What is the total cost of 8 books and 5 pens?

    <p>420 rupees</p> Signup and view all the answers

    The ratio of incomes of the two persons is 9:7.

    <p>True</p> Signup and view all the answers

    What is the area change if the length of a rectangle is reduced by 5 units and the breadth is increased by 3 units?

    <p>-8 square units</p> Signup and view all the answers

    The distance between places A and B is _____ kilometers.

    <p>70</p> Signup and view all the answers

    Match the financial terms with their definitions:

    <p>Savings = Money set aside for future use Investments = Assets purchased to generate income Income Tax = Tax imposed on individual earnings Financial Planning = Process of managing finances for future goals</p> Signup and view all the answers

    What happens to the fraction if the numerator is multiplied by 3 and 3 is subtracted from the denominator?

    <p>It becomes 18</p> Signup and view all the answers

    If both cars travel towards each other, they meet after 1 hour.

    <p>True</p> Signup and view all the answers

    How much do both persons save?

    <p>200 rupees each</p> Signup and view all the answers

    Study Notes

    Ratio and Proportion

    • Ratio compares two quantities by division. A ratio is written as a:b or a/b.
    • Proportion is an equality of two ratios.
    • Properties of ratios:
      • The ratio a:b can be expressed as ka:kb, where k is a non-zero constant.
      • The ratio a/b is unchanged if both a and b are multiplied or divided by the same non-zero value.
    • Theorem of Equal Ratios: If a/b = c/d = e/f, then (a+c+e)/(b+d+f) = a/b.
    • The k-method: If a/b = c/d = e/f = k, then a = bk, c = dk, e = fk.
    • Direct proportion. Two quantities are directly proportional if an increase in one causes a proportional increase in the other, and vice-versa.
    • Inverse proportion. Two quantities are inversely proportional if an increase in one causes a proportional decrease in the other, and vice-versa.

    Properties of Ratio

    • Ratio of two numbers a and b is a:b or a/b, where 'a' is the first term, and 'b' is the second term.
    • In the ratio a/b, if b = 100, then it is a percentage. e.g., 2/100 = 2%
    • The ratio remains unchanged if the terms are multiplied or divided by the same non-zero value. e.g., 3 : 4 = 6:8 = 9:12
    • The quantities taken in the ratio must be in the same units.
    • The ratio of two quantities is dimensionless.
    • If a/b = c/d, then ad = bc.

    Comparison of Ratios

    • The numbers a, b, c, d being positive, comparison of ratios a/b and c/d can be done using the following rules:
      • If ad > bc, then a/b > c/d
      • If ad < bc, then a/b < c/d
      • If ad = bc, then a/b = c/d

    Operations on Equal Ratios

    • Invertendo: If a/b = c/d, then b/a = d/c
    • Alternando: 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-dividendo: If a/b = c/d, then (a + b)/(a - b) = (c + d)/(c - d)

    Continued Proportion

    • If a, b, and c are in continued proportion, then a/b = b/c = k.
    • In this case, b is the geometric mean of a and c and b² = ac.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    Ratio and Proportion PDF

    Description

    This quiz tests your knowledge on proportions, ratios, and variations in mathematics. It includes questions about direct variation, methods of relating variables, and practical applications such as calculating speed, weight, and ratios. Perfect for students looking to strengthen their understanding of mathematical relationships.

    More Like This

    Ratios and Proportions Quiz
    5 questions

    Ratios and Proportions Quiz

    ConstructiveKunzite avatar
    ConstructiveKunzite
    Mathematical Ratios and Proportions Quiz
    9 questions

    Mathematical Ratios and Proportions Quiz

    AdroitMilkyWay avatar
    AdroitMilkyWay
    Understanding Proportions and Ratios
    15 questions

    Understanding Proportions and Ratios

    LaudableTuring5607 avatar
    LaudableTuring5607
    Direct Proportion and Ratios Quiz
    14 questions

    Direct Proportion and Ratios Quiz

    InstrumentalTragedy3462 avatar
    InstrumentalTragedy3462
    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser