Tag: direct proportion and inverse proportion

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)