Tag: inverse proportion

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Questions Related to 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.