Tag: direct proportion and inverse proportion

Quizzes (3) Questions (59)

Questions Related to direct proportion and inverse proportion

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

Present ages of $X\;and\;Y$ are in the ratio $5\,\colon\,6$ respectively. Seven years hence this ratio will become $6\,\colon\,7$ respectively. What is $X's$ present age ?

  1. $35$ years
  2. $42$ years
  3. $49$ years

  4. Can't be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

As per question,
$\frac { x }{ y } =\frac { 5 }{ 6 } $
$6x=5y$
$6x-5y=0$  multiply eq by 6.
$36x-30y=0$  ...eq 1
$\frac { x+7 }{ y+7 } =\frac { 6 }{ 7 } $
$7x+49=6y+42$  
$7x-6y=-7$  ...multiply eq by 5.
$35x-30y=-35$.... eq 2
eq1-eq2
$x=35$
Answer (A) 35 Years


Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions
 $x$ $ 2$  $4$ $ 20$  $15$
 $y$  $3$  $7$ $ 10$  $12$
 $z$  $10$ $ 5$ $ 1$  $4/3$

Observe the table and find the quantities which are in inverse proportion

  1. $x \ and \ y$
  2. $x \ and \ z$
  3. $y \ and \ z$

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By definition of inverse proportion,

$a \  \alpha \  \dfrac{1}{b}$ i.e. $a = K \dfrac{1}{b}$                $K=$ constant of proportionality
$\therefore a\times b = K$  
From given example, consider
$x \times y =2\times 3 \neq 4\times 7 \neq 20\times 10\neq 15\times 12$
$x\times z = 2\times 10 = 4\times 5 = 20\times 1 = 15\times \dfrac{4}{3} = 20$
$\therefore$ $x$ and $z$ obey the equation $1$
Hence $x$ and $z$ are in inverse proportion.
Answer is B

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions
$ x$  $2$ $ 5$ $ 25$
$ y$  $25$  $10$  $m$

If $x$ & $y$ are in inverse proportion, find m

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The given example is of inverse proportion.

by definition, 
$x\propto \dfrac{1}{y}$ i.e. $x = K\dfrac{1}{y}$ , where $K$ is constant of proportionality
$\therefore xy = K$
$x\times y = 2\times 25 = 50 = K$
now, $25\times m = 50$
$\therefore m = 2$
Answer is option B

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions
 $x$  $2$ $ 3$ $ 5$ $ 6$ $10$
$ y$  $15$  $10$ $ b$  $5$ $ 3$

Identify the inverse proportional quantities.

  1. $4$
  2. $5$
  3. $6$
  4. $10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The given example is of inverse proportion.

by definition, 
$x\propto \dfrac{1}{y}$ i.e. $x = K\dfrac{1}{y}$ , where $K$ is constant of proportionality
$\therefore xy = K$
$x\times y = 2\times 15 = 30 = K$
now, $5\times b = 30$
$\therefore b = 6$
Answer is option C

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

If $\displaystyle \frac { a }{ b } -\frac { c }{ d } =0$ and bc=7, then determine the true statement among the following.

  1. a and b are directly proportional.

  2. a and c are inversely proportional.

  3. a and d are inversely proportional.

  4. b and c are directly proportional.

  5. c and d are inversely proportional.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $\dfrac{a}{b}-\dfrac{c}{d}=0$

$\Rightarrow \dfrac{a}{b}=\dfrac{c}{d}$
$\Rightarrow ad=bc$
According to the question $bc=7$
$\therefore ad=7$
Then $a$ and $d$ are inversely proportional to eachother.