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Direct and Inverse Proportions MATHS - Direct and Inverse Proportions

Gujarat Board (GSEB) - STD 8 - MATHS (GSEB - English Medium). 77 questions in this chapter.

Question types

Direct and Inverse Proportions question types

77 questions across 7 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

77
Questions
7
Question groups
5
Question types
Sample Questions

Direct and Inverse Proportions questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 2M.C.Q. [1 Marks Each]1 Mark
Tick $(\checkmark)$ the correct answer in the folllowing: A car is travelling at a uniform speed of $75\ km/hr.$ How much distance will it cover in $20$ minutes$?$
  • ✓
    $25\ km$
  • B
    $15\ km$
  • C
    $30\ km$
  • D
    $20\ km$

Answer: A.

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Q 3M.C.Q. [1 Marks Each]1 Mark
Tick $(\checkmark)$ the correct answer in the folllowing: A photograph of a bacteria enlarged $50000$ times attains a length of $5\ cm.$ The actual length of bacteria is:
  • A
    $ 1000 \mathrm{~cm} $
  • B
    $ 10^{-3} \mathrm{~cm} $
  • ✓
    $ 10^{-4} \mathrm{~cm} $
  • D
    $ 0^{-2} \mathrm{~cm} $

Answer: C.

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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): If $x$ and $y$ are in direct proportion then $\frac{1}{x}$ and $\frac{1}{y}$ are also in direct proportion. 
Reason (R): If $x$ increases then $\frac{1}{x}$ decreases and if $y$ increases then $\frac{1}{y}$ decreases.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.

Answer: B.

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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): If 25 persons can finish a job in 10 days then 5 persons will finish it in 2 days. 
Reason (R): More persons, lesser is the time taken to do the job.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is false but Reason (R) is true.

Answer: D.

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Q 8Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): If $x$ and $y$ are inversely proportional then $x y=k$, where $k$ is a positive constant.
Reason (R): In inverse proportion, as the value of $x$ increases the value of $y$ decreases.
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.

Answer: A.

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Q 9Assertion (A) & Reason (B) MCQ1 Mark
Assertion (A): The height and weight of individuals are in direct proportion. 
Reason (R): Height to weight ratio varies from one individual to another.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is false but Reason (R) is true.

Answer: D.

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Q 102 Marks Questions2 Marks
Observe the tables given below and in each case find whether $x$ and $y$ are inversely proportional.
$x$ $5$
$9$
$15$
$16$
$y$
$9$
$15$
$21$
$24$
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Q 112 Marks Questions2 Marks
Observe the tables given below and in each one find whether $x$ and $y$ are proportional.
$x$ $2.5$ $4$ $7.5$ $10$ $14$
$y$ $10$ $16$ $30$ $40$ $42$
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Q 132 Marks Questions2 Marks
Observe the tables given below and in each one find whether $x$ and $y$ are proportional.
$x$ $5$ $7$ $9$ $15$ $18$ $25$
$y$ $15$ $21$ $27$ $60$ $72$ $75$
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Q 142 Marks Questions2 Marks
Observe the tables given below and in each case find whether $x$ and $y$ are inversely proportional.
$x$
$6$
$10$
$14$
$16$
$y$
$9$
$15$
$21$
$24$
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Q 163 Marks Question3 Marks
A car takes $5$ hours to reach a destination by travelling at the speed of $60\ km/hr.$ How long will it take when the car travels at the speed of $75\ km/hr?$
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Q 205 Marks Questions5 Marks
If $x$ and $y$ are inversely proportional, find the values of $x _1, x _2, y _1$ and $y _2$ in the table given below.
$x$ $8$
$x_1$
$16$
$x_2$
 $80$
$y$
$y_1$
$4$
$5$
$2$
 $y_2$
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Q 21Case study (4 Marks)4 Marks
Three quantities $x, y$ and $z$ are such that $x$ and $y$ are directly proportional to each other while $y$ and $z$ are inversely proportional to each other. If $x=12$ then $y=72$ and $z=8$.

(1) If $y=42$ then $x$ is equal to
(a) 6
(b) 7
(c) 8
(d) 10

(2) If $z=12$ then $y$ is equal to
(a) 36
(b) 48
(c) 60
(d) 64

(3) Which of the following cannot be a possible combination of the values of $x$ and $y$ ?
(a) 6.5 and 39
(b) 9 and 54
(c) 47 and 282
(d) 52 and 260

(4) If $x=24$ then $z$ is equal to
(a) 4
(b) 6
(c) 8
(d) 12
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