Tag: direct proportion

Questions Related to direct proportion

$4$ 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}$
$n _{2} = 200$

If 18 pumps can raise 2170 tonnes of water in 10 days, working 7 hours a day then in how many days will 16 pumps raise 1736 tonnes of water, working 9 hours a day ?

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

  1. 6

  2. 7

  3. 8

  4. 9

Show answer
Correct Option: B
Explanation:

Let the required number of days be x.
 Then,

Less pumps, More days (Indirect Proportion)


Less water, Less days (Direct Proportion)


More hours / day, Less days (Indirect Proportion)
 Pumps 8 : 9


Weight 1085 : 868
 Hours/day 9 : 7 :: 10 : x
$ (8 \times  1085 \times  9 \times  x) = (9 \times  868 \times  7 \times  10)$
$ x = (9 \times  868 \times  7 \times  10)/(8 \times  1085 \times  9)$
$ x=7 $
Answer (B) 7

If $a : b = 5 : 9$ and $b : c = 4 : 7$ find $a : b : c$

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

  1. $5:9:\dfrac{63}{4}$

  2. $20:63:36$

  3. $4:36:63$

  4. $20:36:63$

Show answer
Correct Option: A,D
Explanation:

Given, $a : b = 5 : 9 $ and $b : c = 4 : 7$ $=$ $\displaystyle \left ( 4\times

\frac{9}{4} \right ):\left ( 7\times \frac{9}{4} \right

)=9:\frac{63}{4}$
$\displaystyle \Rightarrow a:b:c=5:9:\frac{63}{4}=20:36:63$

Cost of 10 mangoes is Rs. 100 The cost of 18 mangoes is__ 

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

  1. Rs. 18

  2. Rs. 108

  3. Rs. 200

  4. Rs. 180

Show answer
Correct Option: D
Explanation:

The cost of mangoes is directly proportional to the number of mangoes bought.

So, if $ 10 $ mangoes costs $ Rs\  100 $, then $ 1 $ mango will cost $ Rs \dfrac{ 100 }{10}  = Rs  10 $

And $ 18 $ mangoes will cost $ 18 \times Rs \dfrac{ 100 }{10}  = Rs 180 $

14 apples cost Rs. 140 The cost of 1 apple is__

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

  1. Rs. 10

  2. Rs. 8

  3. Rs. 4

  4. Rs. 14

Show answer
Correct Option: A
Explanation:

The cost of apples is directly proportional to the number of apples bought.

So, if $ 14 $ apples cost $ Rs\  140 $, then $ 1 $ apple will cost $ Rs \dfrac{ 140 }{14}  =  Rs  10 $