A group of students can complete a project in 12 days. If 4 more students join,
Practice Questions
Q1
A group of students can complete a project in 12 days. If 4 more students join, the project can be completed in 8 days. How many students were initially in the group? (2023)
6
8
10
12
Questions & Step-by-Step Solutions
A group of students can complete a project in 12 days. If 4 more students join, the project can be completed in 8 days. How many students were initially in the group? (2023)
Step 1: Let the initial number of students be represented by 'x'.
Step 2: Understand that the total work done is the same in both scenarios.
Step 3: In the first scenario, the work done by 'x' students in 12 days can be expressed as 'x * 12'.
Step 4: In the second scenario, when 4 more students join, the total number of students becomes 'x + 4'.
Step 5: The work done by 'x + 4' students in 8 days can be expressed as '(x + 4) * 8'.
Step 6: Set the two expressions for work equal to each other: 'x * 12 = (x + 4) * 8'.
Step 7: Expand the right side of the equation: 'x * 12 = 8x + 32'.
Step 8: Rearrange the equation to isolate 'x': '12x - 8x = 32'.
Step 9: Simplify the equation: '4x = 32'.
Step 10: Divide both sides by 4 to solve for 'x': 'x = 8'.
Work and Time – This problem tests the understanding of the relationship between the number of workers, the time taken to complete a task, and the total work done.
Algebraic Manipulation – The question requires setting up and solving a linear equation based on the given conditions.
