Chain RulePoints to Remember1) Direct Proportion:
Any two quantities are said to be directly proportional, if on the increase of one quantity, the other quantity increases and vice-versa.Example:
Cost is directly proportional to number of objects
Cost ∝ Number of objects
Number of objects increases (↑) Cost (↑)Example:
Work done is directly proportional to number of working men
Work done ∝ Number of working men
Number of men increase (↑) Work done (↑)2) Indirect Proportion:
Any two quantities are said to be indirectly proportional, if on the increase of one quantity, the other quantity decreases and vice-versa.Example:
If speed of car is increases, then the time required to cover the distance decreases.
Speed of car (↑) Time required decreases (↓)Example:
Time taken to finish work increases, if number of men decrease.
Time (↑) Number of men (↓)Tips and Tricks
In this chapter generally different types of numerical related to time and work, time and speed, cost and number of articles, men and work, etc. are asked.
Q 1. If 30 men can do a piece of work in 20 hours, then in how many hours will 12 men do it?
Type 1: Indirect proportion
a. 18 hours
b. 30 hours
c. 40 hours
d. 50 hoursView solution
Correct Option: (d)12 men require 50 hours to complete the same work.
Hint: As number of workers increase, the time required decreases. Hence, this is a problem related to indirect proportion.
Workers (↑),Time (↓)
Let the number of hours be x.
12 : 30 :: 20 : x
3 pumps, working 4 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work, to empty the tank in one day?
a. 7 hours
b. 8 hours
c. 6 hours
d. 5 hoursView solution
Correct Option: (c)
Hint: As number of pumps increase, the time required decreases and when working hours increase, fewer days are required to complete the work. Hence, this is a problem related to indirect proportion.
Given: 3 pumps can empty a tank in 2 days, if they are working 6 hours a day
Find: Number of hours a day, 3 pumps must work, to empty the tank in one day.
More pumps (↑),Less working hours (↓)
More working hours (↑),Less days (↓)
|4 : x :: ||Pumps are in the ratio 4 : 3|
|Days are in the ratio 1 : 2|
4 × 3 × 2 = 4 × 1 × x
24 = 4x
x = 6 Alternate solution 1: (Trick)
Arrange all given parameters in table format.
Simply multiply, we get
3 × 2 × 4 = 4 × 1 × A
Alternate solution 2:
|A = ||3 × 2 × 4|| = 6 hrs|
|4 × 1|
We are given that, 3 pumps, working 4 hours a day, can empty a tank in 2 days. Therefore, it means that:
3 pumps take total 8 hours to empty the tank.Hence, 1 pump will take 8 x 3 = 24 hours Remember: As number of pump decrease, time required increases. So, if 4 pumps work, time required decreases.
A wheel that has 6 cogs is meshed with a larger wheel of 12 cogs. If the smaller wheel has made 22 revolutions, then find the number of revolutions made by the larger wheel.
d. 17View solution
Correct Option: (a)
Hint: As number of cogs increase, the revolutions made decrease. Hence, this is a problem related to indirect proportion.
Let the number of wheels be x.
More cogs (↑),Less revolutions (↓)
Given: 6 cogs meshed with wheel of 12 cogs and smaller wheel made 22 revolutions
12:6 :: 22:x
12 × x=6 × 22