General Questions

Let the required number of bottles be x.

More machines, More bottles (Direct Proportion)

More minutes, More bottles (Direct Proportion)

Machines	6	:	10		:: 270 : x
Time (in minutes)	1	:	4

6 x 1 x x = 10 x 4 x 270

x =	(10 x 4 x 270)
	(6)

x = 1800.

Let the required number of bottles be x.

More machines, More bottles (Direct Proportion)

More minutes, More bottles (Direct Proportion)

Machines	6	:	10		:: 270 : x
Time (in minutes)	1	:	4

6 x 1 x x = 10 x 4 x 270

x =	(10 x 4 x 270)
	(6)

x = 1800.

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)

Pumps	4	:	3		:: 8 : x
Days	1	:	2

4 x 1 x x = 3 x 2 x 8

x =	(3 x 2 x 8)
	(4)

x = 12.

Cost of x metres = ₹ d.

Cost of 1 metre = ₹		d
		x

Cost of y metres = ₹		d	. y		= ₹		yd	.
		x					x

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 x 35
	125

x = 42.

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

Then, More cogs, Less revolutions (Indirect Proportion)

14 : 6 :: 21 : x       14 x x = 6 x 21

x =	6 x 21
	14

x = 9.

Let the required weight be x kg.

Less weight, Less cost (Direct Proportion)

250 : 200 :: 60 : x       250 x x = (200 x 60)

x=	(200 x 60)
	250

x = 48.

Let the required number days be x.

Less spiders, More days (Indirect Proportion)

Less webs, Less days (Direct Proportion)

Spiders	1	:	7		:: 7 : x
Webs	7	:	1

1 x 7 x x = 7 x 1 x 7

x = 7.

Balance work =		1 -	5		=	3
			8			8

Let the required number of days be x.

Then,	5	:	3	= :: 10 : x		5	x x =	3	x 10
	8		8			8		8

x =		3	x 10 x	8
		8		5

x = 6.

Let the required number of days be x.

Less cows, More days (Indirect Proportion)

Less bags, Less days (Direct Proportion)

Cows	1	:	40		:: 40 : x
Bags	40	:	1

1 x 40 x x = 40 x 1 x 40

x = 40.