Tag: direct proportion and inverse proportion

Questions Related to direct proportion and inverse proportion

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 ?

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

  1. $35$ years

  2. $42$ years

  3. $49$ years

  4. Can't be determined

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Correct Option: A
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


 $x$ $ 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

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

  1. $x \ and \  y$

  2. $x \ and \ z$

  3. $y \ and \ z$

  4. None of the above

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Correct Option: B
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

$ x$  $2$ $ 5$ $ 25$
$ y$  $25$  $10$  $m$

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

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

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: B
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

Which of the following $x$ & $y$ are in inverse proportion?

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

  1. $\dfrac{x}{y}=K$

  2. $x+y=K$

  3. $x-y=K$

  4. $xy=K$

Show answer
Correct Option: D
Explanation:
 $\dfrac{x}{y}=k$$\implies x=ky$$\implies x\alpha y$  $x+y=k$$\implies x=k-y$  $x-y=k$$\implies x=k+y$ $xy=k$$\implies x=\dfrac{k}{y}$$\implies x\alpha \dfrac{1}{y}$ 

Answer $(D)$

 $x$  $2$ $ 3$ $ 5$ $ 6$ $10$
$ y$  $15$  $10$ $ b$  $5$ $ 3$

Identify the inverse proportional quantities.

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

  1. $4$

  2. $5$

  3. $6$

  4. $10$

Show answer
Correct Option: C
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

Find inverse proportionaly constant if $x$ and $y$ are in inverse proportion.

$x$ $9$ $6$ $3$ $18$
$y$ $2$ $3$ $6$ $1$
maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

  1. $9$

  2. $18$

  3. $27$

  4. $30$

Show answer
Correct Option: B
Explanation:

$\because x$ and $y$ are inverse porportion
$\therefore x \times y = k \Rightarrow 9\times 2 = 6\times 3 = 3\times 6 = 18\times 1 = 18 = k$

A work is done by $10$ workers in $6$ hours? How many workers will be required to do the same work in $4$ hrs?

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

  1. $10$

  2. $15$

  3. $20$

  4. None of these

Show answer
Correct Option: B
Explanation:

It is inverse variation.
$6\times 10 = 4\times x$
$\Rightarrow x = \dfrac {6\times 10}{4} = 15\ workers$

$35$ workers can build a house in $16$ days. How many days will $28$ workers working at the same rate take to build the same house?

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

  1. $16\ days$

  2. $28\ days$

  3. $20\ days$

  4. $10\ days$

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Correct Option: C
Explanation:

By inverse proportion,

$28\times x = 35\times 16$

$x = \dfrac {35\times 16}{28} = 20\ days$

Four pipes can fill a tank in $70$ min. How long will it take to fill the tank by $7$ pipes?

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

  1. $20\ min$

  2. $35\ min$

  3. $40\ min$

  4. None of these

Show answer
Correct Option: C
Explanation:

By the principle of inverse proportion
$4\times 70 = 7\times x$
$\Rightarrow x = \dfrac {4\times 70}{7} = 40\ min$

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

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

  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.

Show answer
Correct Option: C
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.