Let the required number of working hours per day be x.

More pumps, Less working hours per day (Indirect Proportion)

Less days, More working hours per day (Indirect Proportion)

So, 4 x 1 x x = 3 x 2 x 8

x = \(\frac{(3\times2\times8)}{(4)}\)

x = 12.

Cost of x metres = Rs. d.

Cost of 1 metre = Rs. \(\left(\frac{d}{x}\right)\)

Cost of y metres = Rs.  \(\left(\frac{d}{x}.y\right)\)   = Rs.  \(\left(\frac{yd}{x}\right)\)

Let the required number of bottles be x.

More machines, More bottles (Direct Proportion)

More minutes, More bottles (Direct Proportion)

So,  6 x 1 x x = 10 x 4 x 270

x = \(\frac{(10\times4\times270)}{(6)}\) 

x= 1800.

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)

So,  125 : 150 :: 35 : x   \(\Leftrightarrow\)     125 x x = 150 x 35

x = \(\frac{150\times35}{125}\)

x = 42.

Let the required number of days be x.

Less persons, More days (Indirect Proportion)

More working hours per day, Less days (Indirect Proportion)

30 x 6 x x = 39 x 5 x 12

x = \(\frac{(39\times5\times12)}{(30\times6)}\)

x =13.

Work done = \(\frac{5}{8}\)

Balance work = \(\left(1-\frac{5}{8}\right)=\frac{3}{8}\)

Let the required number of days be x.

Then, \( \frac{5}{8}:\frac{3}{8}=::10:x \Leftrightarrow \frac{5}{8}\times x =\frac{3}{8}\times10\)

x = \(\left(\frac{3}{8}\times10\times\frac{5}{8}\right) \)

x= 6.

Let the required weight be x kg.

Less weight, Less cost (Direct Proportion)

So,  250 : 200 :: 60 : x   \(\Leftrightarrow \)    250 x x = (200 x 60)

x = \(\frac{(200\times60)}{250}\)

x = 48.

Let the required number of days be x.

Less cows, More days (Indirect Proportion)

Less bags, Less days (Direct Proportion)

1 x 40 x x = 40 x 1 x 40

x = 40.

Let the required number of revolutions made by larger wheel be x.

Then, More cogs, Less revolutions (Indirect Proportion)

So,  14 : 6 :: 21 : x   \( \Leftrightarrow\)   14 x x = 6 x 21

x =  \(\frac{6\times21}{14}\)

x  = 9.

Let the required number days be x.

Less spiders, More days (Indirect Proportion)

Less webs, Less days (Direct Proportion)

1 x 7 x x = 7 x 1 x 7

x = 7.