FACTS  AND  FORMULAE  FOR  CHAIN  RULE  QUESTIONS

 

 

1. Direct Proportion: Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent.

Ex. 1. Cost is directly proportional to the number of articles. (More Articles, More Cost)

Ex. 2. Work done is directly proportional to the number of men working on it (More Men, More Work)

 

2. Indirect Proportion: Two quantities are said to be indirectly proportional,if on the increase of the one, the other decreases to the same extent and vice-versa.

Ex. 1. The time taken by a car in covering a certain distance is inversely proportional to the speed of the car. (More speed, Less is the time taken to cover a distance)

Ex. 2. Time taken to finish a work is inversely proportional to the num of persons working at it. (More persons, Less is the time taken to finish a job)

Q:

Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in

A) 6 days B) 12 days
C) 4 days D) 3 days
 
Answer & Explanation Answer: D) 3 days

Explanation:

Let x men can do the in 12 days and the required number of days be z

 

More men, Less days     [Indirect Proportion]

 

Less work, Less days     [Direct Proportion  ]

 men2x:xwork1:12 :: 12 : z

2x×1×z=x×12×12

 z=3

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25 21491
Q:

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 & Explanation Answer: B) 9

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*21/14  =>  x=9

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18 21201
Q:

If 36 men can do a piece of work in 25 hours, in how mwny hours will15 men do it?

A) 40 B) 50
C) 60 D) 70
 
Answer & Explanation Answer: C) 60

Explanation:

Let the required no of hours be x. Then

 

Less men , More hours    (Indirct Proportion)

 

Therefore,  15:36 ::25:x 

=> (15 x X)=(36 x 25)  => x = 60

 

Hence, 15 men can do it in 60 hours.

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79 19913
Q:

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 & Explanation Answer: A) 48 Paise

Explanation:

Let the Required cost be X paise.  Less Weight , Less cost (Direct Proportion)

Therefore, 250 : 200 :: 60 : x

=> (250 * x) = (200 * 60)

=> x= 48

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12 16794
Q:

If 18 bindres bind 900 books in 10 days , How many binders will be required to bind 660 books in 12 days?

A) 22 B) 14
C) 13 D) 11
 
Answer & Explanation Answer: D) 11

Explanation:

Let the required no of binders be X.

Less books , Less binders       (Direct Proportion)

More days, Less binders         (Indirect proportion)

 

 Books900:660Days12 : 10 18:x

Therefore, (900 * 12 * x) =  (660 * 10 * 18)  

=> x = 11

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33 15504
Q:

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 & Explanation Answer: D) Rs. (yd/x)

Explanation:

Cost of x metres = Rs. d.

Cost of 1 metre = Rs.(d/x)

Cost of y metres = Rs.[(d/x).y] = Rs.(yd/x)

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12 13017
Q:

If 8 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days?

A) 350 B) 400
C) 425 D) 450
 
Answer & Explanation Answer: D) 450

Explanation:

Let the required no of hectares be x. Then 

More men, More hectares      (Direct proportion)

More days, More hectares      (Direct proportion)

 Men8 : 36Days24:30 80 :x

=> ( 8 * 24 * x) = (36 * 30 * 80)

=>  x= 450

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20 11306
Q:

 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 & Explanation Answer: C) 40

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:xbags   40:1 :40:x

 

1 x 40 x x = 40 x 1 x 40

 

=>  x = 40.

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9 10333