Tag: direct proportion and inverse proportion

Questions Related to direct proportion and inverse proportion

If $a:b=c:d$ then how many of the following statements are true?

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

  1. $c(a+b)=a(c+d)$

  2. $d(a-b)=b(c-d)$

  3. $(a^{2}+b^{2})(ac-bd)=(a^{2}-b^{2})(ac+bd)$

  4. $(a^{2}-b^{2})(ad-bc)=(a^{2}+b^{2})(ac-bd)$

Show answer
Correct Option: A
Explanation:

$\dfrac{a}{b}=\dfrac{c}{d}$
$\dfrac{b}{a}=\dfrac{d}{c}$

$\left(1+\dfrac{b}{a}\right)=\left(1+\dfrac{d}{c}\right)$
$\dfrac{(a+b)}{a}=\dfrac{(c+d)}{c}$
$c(a+b)=a(c+d)$

Mark the correct alternative of the following.
Two numbers are in the ration $3 : 5$ and their sum is $96$. The larger number is?

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

  1. $36$

  2. $42$

  3. $60$

  4. $70$

Show answer
Correct Option: C
Explanation:

Given two numbers are  in the ratio $3:5$.

Let the numbers are $3x$ and $5x$.
Then according to the problem we get,
$3x+5x=96$
or, $8x=96$
or, $x=12$.
So the largest number is $12\times 5=60$.

If $4$ men or $6$ women earn Rs $360$ in one day, then find how much less does a woman earn in one day than men.

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

  1. Rs $20$

  2. Rs $30$

  3. Rs $40$

  4. Rs $35$

Show answer
Correct Option: B
Explanation:

$6$ women earn = Rs $360$ $/day$


$\therefore 1$ woman earns = Rs $\dfrac{360}{6}$ $/day$


                             = Rs $60$ $/day$.
$4$ men earn = Rs $360$ $/day$

$\therefore 1$ man earns = Rs $\dfrac{360}{4}$ $/day$

                             = Rs $90$ $/day$.
$\therefore$ women earn Rs 30 less than man

Eight oranges can be bought for Rs $10.40$, then how many more oranges can be bought for Rs $16.90$?

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

  1. $5$ oranges

  2. $3$ oranges

  3. $7$ oranges

  4. $2$ oranges

Show answer
Correct Option: A
Explanation:

Let $x$ oranges  be bought for Rs.$ 16.90.$


Given, eight oranges are bought for Rs.$ 10.40.$

Then, $\dfrac{8}{x}=\dfrac{10.40}{16.90}$

$\Longrightarrow x=\dfrac{16.90\times 8}{10.40}=13$

Then, $(13-8)=5$ more oranges can be bought.

$4$ men or $6$ women earn Rs $360$ in one day. Find how much will $6$ men and $4$ women earn in one day?

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

  1. Rs $780$

  2. Rs $720$

  3. Rs $760$

  4. Rs $740$

Show answer
Correct Option: A
Explanation:
$6$ women = Rs $360$/day
$4$ women = Rs $360$/day   
One woman  = $x$ Rs/day 
$x = \dfrac { 360 }{ 6 }$  = Rs $60$
 One man = $\dfrac { 360 }{ 4 }$
  = Rs $90$/day.
So,  $6$ men + $4$ women 
$= 6(90) + 4(60)$
$=$ Rs $540$ + Rs $240$
= Rs $780$.

$A$ can do a piece of work in $10$ days and $B$ in $15$ days. How long will they take together to finish it ? 

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

  1. $7$ days

  2. $3$ days

  3. $9$ days

  4. $6$ days

Show answer
Correct Option: D
Explanation:

Work done by A in 1 day $=\dfrac{1}{10}$


Work done by B in 1 day$=\dfrac{1}{15}$

Work done by A and B in 1 day$=\dfrac{1}{10}+\dfrac{1}{15}=\dfrac{25}{150}$

Working together they will complete the work in $\dfrac{150}{25}=6$ days

A sum is divided among four persons in the ratio $3\,\colon\,4\,\colon\,5\,\colon\,8$. If the second largest share is  Rs$\,2500$, what is the total sum?

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

  1. Rs $10000$

  2. Rs $15000$

  3. Rs $1000$

  4. Rs $1500$

Show answer
Correct Option: A
Explanation:

The share is divided in the ratio $3:4:5:8$

$\therefore$ the second largest share is $5$.
Second largest share$\,=\displaystyle\frac{5}{(3+4+5+8)} \times$ Total share 
 $=\displaystyle\frac{5}{20}\times $ Total sum $=\displaystyle\frac{1}{4}\times $  Total sum

Given, second largest share $=Rs.2500$ 
 $\therefore \displaystyle\frac{1}{4}\times$ Total sum $Rs.2500$
 $\Rightarrow$ Total sum $=Rs.10,000$.

One litre of water weighs $1$ kg. How many cubic millimetres of water will weigh $0.1$ gram?

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

  1. $100$ cubic mm.

  2. $150$ cubic mm.

  3. $90$ cubic mm.

  4. $80$ cubic mm.

Show answer
Correct Option: A
Explanation:

$1$ litre $=1000$ cubic cm of water weighs $1000$ g.
$\therefore\,1000$ g is the weight of $(1000\times1000)$ cubic mm ....$(\because\;1$ cm $=10$ mm)
$\therefore\,0.1$ g is the weight of $\displaystyle\frac{1000\times1000}{1000}\times0.1$ cubic mm $=100 $ cu mm.

The cost of $3$ digital cameras and $5$ cell phones is Rs. $35,290$. What is the cost of $9$ digital cameras and $15$ cell phones?

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

  1. Rs. $1,68,450$

  2. Rs. $1,79,220$

  3. Rs. $1,05,870$

  4. None of these

Show answer
Correct Option: C
Explanation:

Cost  of ($3$ digital cameras $+5$ cell phones) $=$Rs $35,290$ 

$\because $ Cost of ($9$ digital cameras $+15$ cell phones) $=3\times$ [cost of( $3$ digital cameras $+5$ cell phones)] 
$=3\times$ Rs. $35,290=$ Rs. $1,05,870$.

A rope makes $260$ rounds of a cylinder with base radius $20$ cm, How many times can it go round a cylinder with base radius $26$ cm?

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

  1. $130$

  2. $300$

  3. $200$

  4. $150$

Show answer
Correct Option: C
Explanation:

Circumference of circular base of cylinder is $2\pi R$.

Total length of the rope $ = n(2 \pi R)$ , where $n$ is number of revolutions 
Since length will remain constant
$n _{1} (2 \pi R _{1}) $ = $n _{2} (2 \pi R _{2}) $
$n _{1} = 260 $ , $n _{2} = ?$, $R _{1} = 20 cm$ and $R _{2} = 26$ cm
$ 260 \times20 = 26 \times n _{2}$
$n _{2} = 200$