Types of proportions - class-VI

Man eat $ 200$ g rice in a day then he  has $35\times 200=7000  g $ rice for  $35$  days
But if he eat  $250$  g rice in a day
Then $7000$  g rice is enough for $\dfrac{7000}{250}=28  \ days$

Let the required price be Rs. x. Then, more mangoes, more price
$\therefore$ $357 : (49 \times 12) :: 1517.25 : x$
$\Rightarrow 357x = (49 \times 12 \times 1517.25)$
$\Rightarrow, x, =, \displaystyle \frac{(49, \times, 12, \times, 1517.25)}{357}, =, 2499$
Hence, the approximate price is Rs. 2500

Let the actural distance be x km. Then, more distance on the map, more is the actual distance. 
$\therefore$ 0.6 : 80.5 :: 6.6 : x
$\Rightarrow, 0.6x, =, 80.5, \times, 6.6$
$\Rightarrow, x, =, \displaystyle \frac{80.5, \times, 6.6}{0.6}, \Rightarrow, x, =, 885.5$

$\dfrac{x}{y}=K;\Rightarrow;\dfrac{20}{y}=4;\Rightarrow;y=\dfrac{20}{4}=5$

2 quantities say it be $x , y$ are said to be in proportion when the change in value of $x$ , leads to the equal change in value of $y$.

By definition of direct proportion,

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

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

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

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

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

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

$1$ 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.

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

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

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

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

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 $

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 $

The distance travelled is directly proportional to the number of hours travelled.

So, if  in $ 4 $ hours, $ 120\ km $ is travelled then in $ 1 $ hour  distance travelled is $  \dfrac{ 120 }{4}\ km $  

And in  $ 6 $ hours, distance travelled is  $ 6 \times \dfrac{ 120 }{4}  = 180\ km $

By definition of proportionality,

Let capacity of drum  $=  x$ litres
Initially, drum was $\dfrac {3x}{4}$ part filled
$30$ litres oil drawn then it become, $\dfrac {7x}{12}$ part.
Now, according to question,
$\dfrac {3x}{4} - \dfrac {7x}{12} = 30$
$\Rightarrow \dfrac {(9x - 7x)}{12} = 30$
$\Rightarrow 2x = 360$
$\Rightarrow x = 180$ litres

Cost of cloth is directly proportional to its length.
$10 = 2\times k \Rightarrow k = 5$    , where k is the cost of cloth per meter
$\therefore$ Cost of $100\ m$ cloth $=5\times 100 = 500$.

$\dfrac{x}{y}=K$ (Direct proportion)

$a$ and $b$ are in direct proportion
$\therefore \dfrac {a}{b} = k = \dfrac {2}{14} = \dfrac {3}{21} = \dfrac {1}{7}$
$\therefore \dfrac {4}{x} = \dfrac {1}{7} \Rightarrow x = 28$.

$\dfrac {a}{b} = \dfrac {3}{9} = \dfrac {7}{21} = \dfrac {10}{30} = \dfrac {11}{33} = \dfrac {1}{3} = k$
$\therefore a$ and $b$ are in direct proportion.

$a\propto \dfrac {1}{b} \Rightarrow a = \dfrac {k _{1}}{b}; k _{1}$ is a constant
$b\propto \dfrac {1}{c} \Rightarrow b = \dfrac {K _{2}}{c}; k _{2}$ is a constant
$\Rightarrow a = \dfrac {k _{1}c}{k _{2}} = k _{3}c; k _{3} = \dfrac {k _{1}}{k _{2}}$ is another constant
$\Rightarrow a\propto c$

Clark's formula is (weight/150) * adult dose. For 75 lbs: (75/150) * 1000 = 500 mg. For 90 lbs: (90/150) * 1000 = 600 mg. The range is 500 to 600 mg, making 500 the only viable option provided.

Let the total work be $72$ units (LCM on $72, 24$ and $36$).

Earning of $4$ men $=$ Rs $360$ per day
Earning of $1$ man $=$ Rs $\dfrac{360}{4}$ per day

Directly proportional: as one amount increases, 
another amount increases at the same rate.
Hence, in option A when number of mangoes in a bag increases,then the weight of the bag also increases.