Chain Rule

Question:
If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

[A].

1

[B].

7

2

[C].

7

[D].

49

Answer: Option C

Explanation:

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.

Question:
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

[A].

9

[B].

10

[C].

11

[D].

12

Answer: Option D

Explanation:

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.

Question:
39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

[A].

10

[B].

13

[C].

14

[D].

15

Answer: Option B

Explanation:

Let the required number of days be x.

Less persons, More days (Indirect Proportion)

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

Persons	30	:	39		:: 12 : x
Working hours/day	6	:	5

30 x 6 x x = 39 x 5 x 12

x =	(39 x 5 x 12)
	(30 x 6)

x = 13.

Question: In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

[A].

1

[B].

1

40

[C].

40

[D].

80

Answer: Option C

Explanation:

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.

Question:
4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

[A].

4

[B].

8

[C].

12

[D].

16

Answer: Option D

Explanation:

Let the required number of bottles be x.

More weavers, More mats (Direct Proportion)

More days, More mats (Direct Proportion)

Wavers	4	:	8		:: 4 : x
Days	4	:	8

4 x 4 x x = 8 x 8 x 4

x =	(8 x 8 x 4)
	(4 x 4)

x = 16.

Question:
In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?

[A].

20

[B].

30

[C].

40

[D].

50

Answer: Option B

Explanation:

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		120	x 50		= 30 men.
		200

Question:
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:

[A].

4

[B].

9

[C].

12

[D].

49

Answer: Option B

Explanation:

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.

Question:
A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:

[A].

29	1
	5

[B].

37	1
	4

[C].

42

[D].

54

Answer: Option C

Explanation:

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.

Question:
36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?

[A].

12

[B].

18

[C].

22

[D].

24

Answer: Option D

Explanation:

Let the required number of days be x.

Less men, More days (Indirect Proportion)

27 : 36 :: 18 : x       27 x x = 36 x 18

x =	36 x 18
	27

x = 24.

Question:
A man completes of a job in 10 days. At this rate, how many more days will it takes him to finish the job?

[A].

5

[B].

6

[C].

7

[D].

7	1
	2

Answer: Option B

Explanation:

Work done =	5
	8

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.