# Chain Rule Questions

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:

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

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.

97 25438
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

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

20 24124
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

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  ]

$∴2x×1×z=x×12×12$

$⇒z=3$

29 23758
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)

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)

20 21710
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

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

15 20276
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

Explanation:

Let the required no of binders be X.

Less books , Less binders       (Direct Proportion)

More days, Less binders         (Indirect proportion)

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

=> x = 11

37 18380
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

Explanation:

Let the required no of hectares be x. Then

More men, More hectares      (Direct proportion)

More days, More hectares      (Direct proportion)

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

=>  x= 450

27 16607
Q:

The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero ?

 A) 14th element B) 9th element C) 12th element D) 7th element

Explanation:

If we consider the third term to be ‘x”
The 15th term will be (x + 12d)
6th term will be (x + 3d)
11th term will be (x + 8d) and
13th term will be (x + 10d).
Thus, as per the given condition, 2x + 12d = 3x + 21d.Or x + 9d = 0.
x + 9d will be the 12th term.

Thus, 12th term of the A.P will be zero.