Aptitude : Chain Rule

1. 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.

2. If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?

A.	Rs. xy d	B.	Rs. (xd)
C.	Rs. (yd)	D.	Rs. yd x

Answer: Option D

Explanation:

Cost of x metres = Rs. d.

Cost of 1 metre = Rs.		d
		x

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

3. Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

A. 648
B. 1800
C. 2700
D. 10800

Answer: Option B

Explanation:

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.

4.       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 willlast, 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.

5. 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.

6. 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.

7. If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?

A. 48 paise
B. 54 paise
C. 56 paise
D. 72 paise


Answer: Option A

Explanation:

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.

8. 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.

9. 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.

10. 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