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:

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) 16 B) 12 C) 8 D) 4

Explanation:

Let the required number of bottles be x.

More weavers, More mats (Direct Proportion)

More days, More mats (Direct Proportion)

4 x 4 x x = 8 x 8 x 4

=> x = $8*8*44*4$

=> x = 16.

7 10260
Q:

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 B) 37 C) 42 D) 54

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

$⇒x=150×35125=42$

15 8809
Q:

An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth ?

 A) 194 seconds B) 195 seconds C) 196 seconds D) 197seconds

Explanation:

Let the time required by x seconds.

Then, More cloth means More time (Direct Proportion)

So, 0.128 : 1 :: 25 : x

$⇒x=1×250.128$ => x = 195.31

So time will be approx 195 seconds

6 8660
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.

29 8399
Q:

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) 50 B) 40 C) 30 D) 20

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 = $12020050$ =30men

7 7898
Q:

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

Explanation:

Let the required number of bottles be x.

More machines, More bottles (Direct Proportion)

More minutes, More bottles (Direct Proportion)

=> 6 * 1 * x = 10 * 4 * 270

=> x= 1800

2 7733
Q:

10 men, working 6 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?

 A) 4 hours a day B) 5 hours a day C) 6 hours a day D) 7 hours a day

Explanation:

More Men, Less Hours {Indirect Proportion}

Less Days, More Hours {Indirect Proportion}

=> 15 * 12 * x = 10 * 18 * 6

=>x = 6

7 7218
Q:

If the Price of 6 toys is Rs. 264.37, What will be the approximate  price of 5 toys?

 A) Rs.120 B) Rs.100 C) Rs.200 D) Rs.220

Explanation:

Let the required Price be Rs. X .Then, Lest toys , Less cost  (Direct Proportion)

Therefore 6 : 5  :: 264.37 : x

=> 6 * x = 5 * 264.37

=> X= 220.308

Therefore,  Approximate price of 5 toys = Rs. 220