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A group of students can complete a project in 12 days. If 4 more students join,

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Question: 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)

Options:

  1. 6
  2. 8
  3. 10
  4. 12

Correct Answer: 8

Exam Year: 2023

Solution: 

Let the initial number of students be x. The work done is constant, so x * 12 = (x + 4) * 8. Solving gives x = 8.

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)
  1. 6
  2. 8
  3. 10
  4. 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.
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