Math Problem Statement

Solve it

3 machines take 4 days to complete a task. How many days will it take for 6 machines to complete the same task?

Solution

The question is in Hindi and seems to involve solving a work-time problem based on the image provided. Let me analyze and solve it.


The problem involves workers and machines. Here's a breakdown of the question:

  1. 3 machines take 4 days to complete the work.
  2. How many days will it take for 6 machines to complete the same work?

Step-by-Step Solution:

  • Step 1: Calculate the total work done.

    If 3 machines complete the work in 4 days: Total work=3×4=12Machine-Days (MD).\text{Total work} = 3 \times 4 = 12 \, \text{Machine-Days (MD)}.

  • Step 2: Work done by 6 machines in 1 day.

    In 1 day, 6 machines will complete: Work done by 6 machines in 1 day=6MD.\text{Work done by 6 machines in 1 day} = 6 \, \text{MD}.

  • Step 3: Days required for 6 machines to complete the total work.

    To complete 12 MD of work: Days required=Total workWork done by 6 machines per day=126=2days.\text{Days required} = \frac{\text{Total work}}{\text{Work done by 6 machines per day}} = \frac{12}{6} = 2 \, \text{days}.

Thus, 6 machines will complete the work in 2 days.


If you'd like to verify or expand the solution further, feel free to ask!

5 Related Questions to Expand Understanding:

  1. How would the solution change if the number of machines increased to 8?
  2. What if only 2 machines were available for the task?
  3. How do we calculate work efficiency for machines in general?
  4. Can you solve this using ratios instead of the detailed method?
  5. How would the answer change if 3 machines worked half the time?

Tip:

Always cross-check your answer by verifying the relationship between work, workers, and time!

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Math Problem Analysis

Mathematical Concepts

Work-Time Relationship
Proportionality

Formulas

Work = Number of Machines × Time
Time = Total Work ÷ Work Per Day

Theorems

Inverse Proportionality of Time and Number of Workers

Suitable Grade Level

Grades 7-9