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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, they can complete it in 8 days. How many students were initially in the group?

Options:

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

Correct Answer: 10

Solution: 

Let the initial number of students be x. The work done is inversely proportional to the number of days. Setting up the equation gives x = 10.

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, they can complete it in 8 days. How many students were initially in the group?
  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, they can complete it in 8 days. How many students were initially in the group?
  • Step 1: Let the initial number of students be x.
  • Step 2: The group can complete the project in 12 days, so the total work can be represented as 'work = students * days'. This means the total work is x * 12.
  • Step 3: When 4 more students join, the total number of students becomes x + 4.
  • Step 4: With the new group of students, they can complete the project in 8 days. So, the total work is also (x + 4) * 8.
  • Step 5: Since the total work remains the same, we can set the two expressions for work equal to each other: x * 12 = (x + 4) * 8.
  • Step 6: Expand the equation: 12x = 8x + 32.
  • Step 7: Subtract 8x from both sides: 12x - 8x = 32, which simplifies to 4x = 32.
  • Step 8: Divide both sides by 4 to find x: x = 32 / 4, which gives x = 8.
  • Step 9: Therefore, the initial number of students in the group is 8.
  • Work and Time Relationship – This concept involves understanding how the number of workers affects the time taken to complete a project, typically using the formula Work = Rate × Time.
  • Algebraic Manipulation – The ability to set up and solve equations based on given conditions, particularly involving variables representing the number of students and days.
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