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Direct And Inverse Proportions Test - 7

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Direct And Inverse Proportions Test - 7
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  • Question 1
    1 / -0
    If x : y = 5 : 3 and 3 : y = 1 : 4, then the value of x is
    Solution
    x : y = 5 : 3



    3x = 5y ... (1)

    Similarly,

    3 : y = 1 : 4



    y = 12

    Put the value of y in (1).

    x = 20
    Hence, option (4) is correct.
  • Question 2
    1 / -0
    If a and b vary inversely with each other, and a = 15 when b = 18, then what will be the value of b when a = 5?
    Solution
    As a and b vary inversely with each other, we can say that
    a × b = constant
    When a = 15 and b = 18, then
    a × b = 15 × 18 = 270
    When a = 5, then
    5 × b = 270

    So, b =
  • Question 3
    1 / -0
    If a varies directly as b2 and a = 8 when b = 3, find the value of a when b = 9.
    Solution
    As a and b2 vary directly, we can say that = constant.
    As per the information given in the question, we have

    a = = 72
    Hence, option (1) is correct.
  • Question 4
    1 / -0
    If , then what is the value of x?
    Solution
    =

    =

    x =

    x = 16

    Hence, option (1) is correct.
  • Question 5
    1 / -0
    x and y are inversely proportional to each other, and when x = 18, y = 6. Which of the following is not a possible pair of corresponding values of x and y?
    Solution
    For inverse proportionality,
    x1y1 = x2y2

    1) 18 × 6 = 9 × 5
    But, 108 ≠ 45

    2) 18 × 6 = 3 × 36
    108 = 108

    3) 18 × 6 = 27 × 4
    108 = 108

    4) 18 × 6 = 9 × 12
    108 = 108

    Hence, option (1) is correct option.
  • Question 6
    1 / -0
    Which of the following statements is incorrect?
    Solution
    (I) Two values are said to be in direct proportion when an increase in one results in an increase in the other. TRUE

    (II) If two values vary inversely with each other, then a1b1 ≠ a2b2. FALSE
    Reason: Whenever two values are inversely proportional to each other, then a1b1 = a2b2.

    (III) If b is inversely proportional to a, then the equation is of the form b = k/a. TRUE

    (IV) If b is directly proportional to a, then the equation is of the form b = ka. TRUE
  • Question 7
    1 / -0
    If x : y = 4 : 9 and y : z = 2 : 5, then what is the value of z : x?
    Solution
    x : y = 4 : 9

    or y = ... (1)
    Now, y : z = 2 : 5



    Now, putting the value of y from equation (1), we get

    =

    =
    =
    =
    Hence, option (4) is correct.
  • Question 8
    1 / -0
    If two variables a and b are in direct proportion, then which of the following equations is correct?
    Solution
    If two variables are in direct proportion, then .
  • Question 9
    1 / -0
    Directions: Read the given statement carefully and answer the question that follows.

    Statement: When one variable increases, the other decreases in proportion so that the product is unchanged.

    Which of the following methods of proportionality is/are followed in the given statement?
    Solution
    In inverse proportion, x1 × y1 = x2 × y2
    Hence, option (1) is correct.
  • Question 10
    1 / -0
    Which of the following are not in inverse proportion?
    Solution
    When the length of the journey by a bus increases, then the price of the ticket also increases.
  • Question 11
    1 / -0
    If 15 workers can build a wall in 48 hours, then how many workers will be required to build the same wall in 24 hours?
    Solution
    Number of workers Time taken to complete the task (in hours)
    15 48
    W 24

    It is a case of inverse proportion.
    ∴ x1y1 = x2y2
    15 48 = W 24
    Or W =
  • Question 12
    1 / -0
    A person earns an interest of Rs. 82 on the principal of Rs. 2400. What amount of interest will he earn if the principal is Rs. 240?
    Solution
    Let the interest be Rs. Y.

    Principal 2400 240
    Interest 82 Y

    The more the principal, the more the interest. So, both are directly proportional to each other.
    We know that the two quantities, x and y, are said to be in direct proportion if they increase or decrease together in such a manner that the ratio of their corresponding values remains constant.
    So, we can say that
    2400 × Y = 240 × 82
    Y = Rs. 8.2
    Hence, option (1) is correct.
  • Question 13
    1 / -0
    In a class, 4 erasers are given to 6 students on sharing basis. How many students are there in the class if 18 erasers are distributed in total?
    Solution
    Let the number of students be Y.

    Number of Erasers 4 18
    Number of Students 6 Y

    The more the number of students, the more the number of erasers we need. So, both are directly proportional.
    We know that the two quantities, x and y, are said to be in direct proportion if they increase or decrease together in such a manner that the ratio of their corresponding values remains constant.
    4 × Y = 6 × 18
    Y = 27
    There are 27 students.
    Hence, option (2) is correct.
  • Question 14
    1 / -0
    In a hostel, food is prepared to feed 250 guests for 20 days. If 50 of them leave the hostel and rent an apartment, then how long would this food last?
    Solution
    Let Y be the number of days the food will last after 50 guests leave.

    Guests 250 200
    Days 20 Y

    This is a case of inverse proportion because as the number of guests decreases, the number of days increases.
    We know that the two quantities, x and y, are said to be in inverse proportion, if an increase in x causes a proportional decrease in y and vice-versa, in such a manner that the product of their corresponding values remains constant.
    So, we can say that
    250 × 20 = 200 × Y
    Y = 25
    Hence, option (1) is correct.
  • Question 15
    1 / -0
    Raju has just enough money to buy 44 bottles worth Rs. 420 each. If the cost of each bottle is increased by Rs. 30, then how many bottles would he be able to buy?
    Solution
    Cost of 1 bottle = Rs. 420
    Cost of 44 bottles = 420 × 44 = Rs. 18,480
    New cost of each bottle = 420 + 30 = Rs. 450
    Number of bottles he can buy at new price = = 41
    Hence, option (3) is correct.
  • Question 16
    1 / -0
    A shopkeeper pays his employee Rs. 600 for 12 days of work. For how many days of work would the employee be paid Rs. 1500?
    Solution
    Let Y be the number of days the employee works for to be paid Rs. 1500.

    Rupees 600 1500
    Days 12 Y

    It is a case of direct proportion.
    We know that two quantities, x and y, are said to be in direct proportion if they increase or decrease together in such a manner that the ratio of their corresponding values remains constant.
    So,



    Y = 30 days
    Hence, option (2) is correct.
  • Question 17
    1 / -0
    A virus, when enlarged 40,000 times under a microscope, attains a length of 4 cm. What is the actual length of the virus?
    Solution
    Let the actual length of the virus be x cm.

    Enlargement 40,000 times 1
    Length 4 cm x

    It is a case of direct proportion.
    We know that two quantities, x and y, are said to be in direct proportion if they increase or decrease together in such a manner that the ratio of their corresponding values remains constant.
    So,

    x = = 10-4 cm
    Hence, option (4) is correct.
  • Question 18
    1 / -0
    Rajan has just enough money to buy 24 pairs of jeans worth Rs. 700 each. How many pairs of jeans can he buy with the same amount if he gets a discount of Rs. 100 on each pair?
    Solution
    Let the number of jeans he can buy at discounted price be x.

    No. of jeans 24 x
    Cost of each pair of jeans Rs. 700 Rs. 600

    It is a case of inverse proportion.
    We know that two quantities, x and y, are said to be in inverse proportion if an increase in x causes a proportional decrease in y and vice-versa, in such a manner that the product of their corresponding values remains constant.
    24 × 700 = (x) × 600
    x = 28
    Hence, option (1) is correct.
  • Question 19
    1 / -0
    3 women can do as much work as 2 men in a given period. If 14 men take 21 days, working 8 hours a day, to complete a piece of work, then how many days would 21 women take to complete the same piece of work, working 6 hours a day?
    Solution
    14 men, working 8 hours a day, complete a piece of work in 21 days.
    Given: Work of 3 women = Work of 2 men
    So, work of 21 women = work of 14 men
    It is a case of inverse proportion.
    x1 × y1 × z1 = x2 × y2 × z2
    i.e.
    14 × 21 × 8 = 14 × y2 × 6
    So, 21 women, working 6 hours a day, will complete the same piece of work in days = 28 days
    Therefore, the correct answer is 28 days.
  • Question 20
    1 / -0
    In 14 days, the concentration of carbon monoxide in the atmosphere becomes 385 ppm. In how many days will it become 495 ppm?
    Solution
    Let X be the number of days in which the carbon monoxide concentration reaches 495 ppm.

    Days 14 X
    Concentration (in ppm) 385 495

    It is a case of direct proportion.
    We know that two quantities, x and y, are said to be in direct proportion if they increase or decrease together in such a manner that the ratio of their corresponding values remains constant.
    So,
    X = x 495
    X = 18 days
    Hence, option (3) is correct.
  • Question 21
    1 / -0
    Directions: Determine whether the given statements are true (T) or false (F) and choose the correct option accordingly.

    1) If x and y are in direct proportion, then = constant.
    2) As the diameter of a circle increases, the circumference also increases. This is a case of direct proportion.
    3) If distance is constant, then work is inversely proportional to force.
    4) In an inverse proportion, if one number increases, then the other will decrease.
    Solution
    1) If x and y are in direct proportion, then = constant.
    This is true because two quantities, x and y, are said to be in direct proportion if they increase or decrease together in such a manner that the ratio of their corresponding values remains constant.

    2) As the diameter of a circle increases, the circumference also increases. This is a case of direct proportion. (True)
    Circumference ∝ Diameter

    3) If distance is constant, then work is inversely proportional to force.
    This is false because: Work = Force x Distance
    If distance is constant, then W = kF.
    So, in this case, work is directly proportional to force.

    4) In an inverse proportion, if one number increases, then the other will decrease.
    This is true because we know that two quantities, x and y, are said to be in inverse proportion if an increase in x causes a proportional decrease in y and vice-versa, in such a manner that the product of their corresponding values remains constant.

    Hence, option (1) is correct.
  • Question 22
    1 / -0
    Fill in the blanks:

    1) When two quantities are in direct proportion, as one increases, the other increases by the same _____.
    2) For some constant k, if xy = k, then the values of x and y vary ____.
    3) When two given quantities vary directly, an increase in one will reflect as ____ in the other quantity.
    Solution
    1) When two quantities are in direct proportion, as one increases, the other increases by the same percentage/value.
    2) For some constant k, if xy = k, then the values of x and y vary inversely.
    3) When two given quantities vary directly, an increase in one will reflect as an increase in the other quantity.
    Hence, option (2) is correct.
  • Question 23
    1 / -0
    Match the following:

    Column 1 Column 2
    1. If the cost of 20 m of cloth is Rs. 540, then the cost to buy 40 m of the same cloth will be Rs. i. 24
    2. If 32 people can finish the stock of fruits in 12 days, then the number of people it will take to finish the stock in 8 days is ii. 48
    3. If 15 girls can do a piece of work in 46 days, then the number of girls it will take to do the same work in 30 days is iii. 23
    4. If Shalini writes 1440 lines in 2 hours, then the number of lines she writes in one minute is iv. 1080
    Solution
    1) Let the required cost be x.

    Cost of Cloth Length of Cloth
    Rs. 540 20 m
    x 40 m

    It is a case of direct proportion.

    So,

    x = 1080 m

    2) Let the required number of people be x.

    Number of People Number of Days
    32 12
    x 8

    It is a case of inverse proportion.
    So, 32 × 12 = x × 8
    x = 48

    3) Let the required number of girls be x.

    Number of Girls Number of Days
    15 46
    x 30

    It is a case of inverse proportion.
    15 × 46 = x × 30
    x = 23

    4) Let the required number of lines be x.

    Number of Lines Time
    1440 2 hours
    (120 minutes)
    x 1 minute

    It is a case of direct proportion.



    x = 12 lines
    Hence, option (2) is correct.
  • Question 24
    1 / -0
    A maid is paid Rs. 248 for 5 days of work.

    1) How much (in Rs.) will she be paid for the whole month of September?
    2) For how many days does she have to work in order to get paid Rs. 2232?
    Solution
    1) Let the amount paid for September be Rs. x.

    Amount 248 x
    Days 5 30

    It is a case of direct proportion.

    So,

    x = Rs. 1488

    2) Let y be the number of working days for which she gets Rs. 2232.

    Amount 248 2232
    Days 5 y

    It is a case of direct proportion.

    So,

    y = 45
    Hence, option (3) is correct.
  • Question 25
    1 / -0
    In which of the following tables are the two quantities (x and y) in inverse proportion?

    1)
    x 6 12 18 48
    y 24 12 8 3


    2)
    x 145 29 40 80
    y 200 1000 725 362.5


    3)
    x 122 244 30.5 15.25
    y 610 1220 152.5 76.25
    Solution
    For two quantities (x and y) to be in inverse proportion, xy = constant.

    1)
    x 6 12 18 48
    y 24 12 8 3

    We need to check if xy = constant.
    6 × 24 = 144
    12 × 12 = 144
    18 × 8 = 144
    48 × 3 = 144
    Hence, the quantities in table 1 are inversely proportional.

    2)
    x 145 29 40 80
    y 200 1000 725 362.5

    We need to check if xy = constant.
    145 × 200 = 29000
    29 × 1000 = 29000
    40 × 725 = 29000
    80 × 362.5 = 29000
    Hence, the quantities in table 2 are inversely proportional.

    3)
    x 122 244 30.5 15.25
    y 610 1220 152.5 76.25

    We need to check if xy = constant.
    122 × 610 = 74420
    244 × 1220 = 297680
    Hence, the quantities in table 3 are not inversely proportional.
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