Chain Rule Questions

Let the required number of days be x.

Less cows, More days (Indirect Proportion)

Less bags, Less days (Direct Proportion)

$$\begin{gathered} cows 1:40 :40:x \\ bags 40:1 :40:x \\ \end{gathered}$$

1 x 40 x x = 40 x 1 x 40

=>  x = 40.

Let the required number of bottles be x.

More weavers, More mats (Direct Proportion)

More days, More mats (Direct Proportion)

$$\begin{gathered} weavers 4:8} :4:x \\ days 4:8}:4:x \end{gathered}$$ 

4 x 4 x x = 8 x 8 x 4

=> x = 8*8*44*4

=> x = 16.

Let the time required by x seconds.

Then, More cloth means More time (Direct Proportion)

So, 0.128 : 1 :: 25 : x

⇒x=1×250.128 => x = 195.31

 So time will be approx 195 seconds

After 10 days : 150 men had food for 35 days.

Suppose 125 men had food for x days.

Now, Less men, More days (Indirect Proportion)

∴ 125 : 150 :: 35 : x    ⇔   125 x x = 150 x 35

 ⇒x=150×35125=42

There is a meal for 200 children. 150 children have taken the meal.

Remaining meal is to be catered to 50 children.

Now, 200 children = 120 men.

50 children = 12020050 =30men

Let the required Price be Rs. X .Then, Lest toys , Less cost  (Direct Proportion) 

Therefore 6 : 5  :: 264.37 : x

=> 6 * x = 5 * 264.37

=> X= 220.308

Therefore,  Approximate price of 5 toys = Rs. 220

Let the required number of bottles be x.

More machines, More bottles (Direct Proportion)

More minutes, More bottles (Direct Proportion)

 machines6:10time(in min)1:4 ⋮⋮ 270:x 

=> 6 * 1 * x = 10 * 4 * 270

=> x= 1800

More Men, Less Hours {Indirect Proportion}

Less Days, More Hours {Indirect Proportion}

 men15 : 10days12 : 18 ⋮⋮ 6:x

=> 15 * 12 * x = 10 * 18 * 6

=>x = 6