Logic Problem Solving

Introduction of solving logic problems:

Logic (from the Greek λογική logikē)[1] is the study of reasoning.[2] Logic is used in most intellectual activity, but is studied primarily in the disciplines of philosophy, mathematics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies. It is one kind of critical thinking. In philosophy, the study of logic falls in the area of epistemology, which asks: "How do we know what we know?" In mathematics, it is the study of valid inferences within some formal language.[3]

-Source Wikipedia

The solving logic problems are given as follow:


Logic problem solving examples:


The examples of logic problem solving are given as follow:

Problem 1:

Roger can mow the lawn in 60 minutes and Sam can mow the lawn in 80 minutes. How long will it take for them to mow the lawn together?

Solution:

Step 1: Let assume variables:

Assume y = Time to mow lawn together

Step 2: Using the formula:

1/s1+1/s2 =1/sa

1/60 + 1/80 = 1/y

Step 3: Solving the equation

Take LCM

60 x 80 =480

To multiply each sides with 480

1/60+1/80 = 1/y

480/60+480/80 = 480/y

8+6 =480/y

14y = 480

Y=480/14 = 34.28

Answer is: The time taken for each of them to mow the lawn together is 34.28 minutes.

Problem 2:

John, Richard and Alexander can complete painting the bench in 3 hours. If John does the job alone he can complete it in 6 hours. If Richard does the job alone he can complete it in 7 hours. How long will it take for Alexander to complete the job alone?

Solution:

Step 1: Let assume variables:

Assume y = time taken by Alexander

Step 2: Using the formula:

1/6 + 1/7 +1/y = 1/3

Step 3: Solving the equation

To multiply both sides with 42y

1/6+1/7+1/y = 1/3

42y/6+42y/7+42/y = 42y/3

7y+6y+42 = 14y

14y-13y = 42

Y = 42

Answer is: The time taken for Alexander to paint the bench alone is 42 hours.


Logic problem solving practice problem:


The logic problem solving practice problems are given as follow:

Problem 3:

C tank can be filled by pipe C in 4 hours and by pipe D in 6 hours. When the tank is full, it can be drained by pipe E in 5 hours. if the tank is initially empty and all 3 pipes are open, how many hours will it take to fill up the tank?

Solution:

Step 1: Let assume variables:

Assume y = time taken to fill up the tank

Step 2: Using the formula:

Pipe C drains the water it is subtracted.

¼+1/6-1/5 =1/y

Step 3: Solving the equation

Take LCM

Multiply both sides with 120

¼+1/6-1/5 = 1/y

120/4+120/6 -120/5 =120/y

30+20-24 = 120/y

26y = 120

Y= 120/26 = 4

Answer: The time taken to fill the tank is 4 x 8/13 hours.