Math Problem Statement
In a market of food stalls there were three food stalls of Ajay, Raj and Mohit who were selling different fast foods and it is found at the end of the day that total 600 customers have visited market. 50% customers purchased from Ajay; 55% customers purchased from Raj; 45% customers purchased from Mohit. 20% of customers who purchased from Ajay also purchased from other two stalls. Customers who purchased from any of two stalls are 190. Customers of only Ajay are 40 more than that of only Raj. Customers who purchased only from Ajay and Raj are 80.
Solution
Let's break down the information and set up equations based on the data provided.
Define:
- Let , , and be the sets of customers who bought from Ajay, Raj, and Mohit, respectively.
Given information:
- Total customers in the market: .
- Customers who bought from Ajay: .
- Customers who bought from Raj: .
- Customers who bought from Mohit: .
- Customers who bought from all three stalls: .
- Customers who bought from any two stalls: .
- Customers who only bought from Ajay are 40 more than those who only bought from Raj.
- Customers who bought only from Ajay and Raj: .
Let's solve step-by-step.
Step 1: Set up the information in equations
Let:
From information given:
- .
- .
- Simplifying, .
- , so .
Step 2: Substitute values
Using :
- gives .
Step 3: Use the remaining information
Let:
- Customers who only bought from Ajay be ,
- Customers who only bought from Raj be ,
- Customers who only bought from Mohit be .
We know:
- .
- From the inclusion-exclusion principle: Substituting known values gives: Simplifying,
Step 4: Solve for individual values of , , and
Using :
- Substitute in :
Now we need further equations or assumptions to solve fully for each
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Math Problem Analysis
Mathematical Concepts
Set Theory
Inclusion-Exclusion Principle
Percentage
Systems of Equations
Formulas
Inclusion-Exclusion Principle: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |C ∩ A| + |A ∩ B ∩ C|
Percentage calculation: Part = (Percentage / 100) * Total
System of equations for solving unknowns
Theorems
Inclusion-Exclusion Principle
Suitable Grade Level
Grades 10-12
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