Math Problem Statement
It looks like you're dealing with a complex problem involving multiple employees working together and individually to complete a task in various amounts of time. To help clarify and solve this, let's break down the information:
Sajid's time is 20% more than Noushad's time. Trilok's time is 50% more than Himanshu's time. Mohan and Lalit can do the work in 36 and 40 days, respectively. Mohan, Himanshu, and Noushad together take 9 days. Lalit, Trilok, and Sajid together take 11.25 days. Budharam, Shivraj, and Vishnu together take 18 days. Budharam's time is 3 times Noushad's time. Shivraj's time is 33.33% more than Trilok's time. Vishnu's time is twice Noushad's time. We can model this problem using algebra to find each individual's time to complete the work alone by setting up equations based on their rates of work (Work = Rate × Time). Let's denote each person's rate of work as 𝑟 𝑋 r X where 𝑋 X is the person's name, and the total work as 𝑊 W. We can use the combined work equations to solve for individual rates. Then, translating these rates into time taken to complete 𝑊 W will allow us to solve the unknowns.
Solution
To solve this complex problem involving multiple employees working together and individually, we will need to set up equations based on their rates of work and the given relationships between their times. Let's denote the time it takes for each person to complete the task individually by:
- : Noushad's time
- : Sajid's time
- : Himanshu's time
- : Trilok's time
- : Mohan's time
- : Lalit's time
- : Budharam's time
- : Shivraj's time
- : Vishnu's time
We know the following:
Relationships between individuals' times:
- (Sajid's time is 20% more than Noushad's time)
- (Trilok's
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Math Problem Analysis
Mathematical Concepts
Algebra
Work and Time
System of Equations
Ratios and Proportions
Formulas
Work = Rate × Time
Rate of work (individual) = 1/time taken by the individual
Combined rate of work = sum of individual rates of work
Theorems
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Suitable Grade Level
Grades 9-12