Project Contribution Ratio Explained

In this problem, we need to determine the ratio of contribution between two team members, M and E, working on a project. Their contributions are influenced by their individual efficiencies, the number of hours they work per day (shift duration), and the total number of days they work. Understanding these factors is crucial for an accurate calculation of their project contributions.

Understanding Worker Efficiency

The question provides specific information about the efficiency of each team member. Let's define their efficiencies relative to each other:

• The efficiency of S, E, and F is considered as a base unit. Let's assume their efficiency is \(\text{1 unit of work per hour}\).
• M works with twice the efficiency of others. Therefore, M's efficiency is \(\text{2 units of work per hour}\).

Daily Shift Hours and Workdays

The daily working hours (shift duration) and the total days worked vary for different team members. This directly impacts their total contribution to the project.

• Daily Shift Hours:
  • S and M have 6-hour shifts in a day.
  • E and F have 12-hour shifts in a day.
• Total Workdays:
  • Let's assume E worked for a total of \(D\) days on the project.
  • M worked for half as many days as E. So, M worked for \(\frac{D}{2}\) days.

Calculating Individual Contributions

The total contribution of an individual to a project can be calculated by multiplying their efficiency, their daily working hours, and the total number of days they worked. The formula for contribution is:

\[ \text{Contribution} = \text{Efficiency per hour} \times \text{Hours per day} \times \text{Number of days worked} \]

M's Project Contribution

Let's calculate the contribution of M based on the information gathered:

• M's Efficiency = \(\text{2 units/hour}\)
• M's Daily Shift = \(\text{6 hours/day}\)
• M's Days Worked = \(\frac{D}{2}\) days

Using the contribution formula:

\[ \text{Contribution of M} = 2 \text{ units/hour} \times 6 \text{ hours/day} \times \frac{D}{2} \text{ days} \]

\[ \text{Contribution of M} = \left( 2 \times 6 \times \frac{1}{2} \right) D \text{ units} \]

\[ \text{Contribution of M} = 6D \text{ units} \]

E's Project Contribution

Now, let's calculate the contribution of E:

• E's Efficiency = \(\text{1 unit/hour}\) (since E's efficiency is like others)
• E's Daily Shift = \(\text{12 hours/day}\)
• E's Days Worked = \(D\) days

Using the contribution formula:

\[ \text{Contribution of E} = 1 \text{ unit/hour} \times 12 \text{ hours/day} \times D \text{ days} \]

\[ \text{Contribution of E} = \left( 1 \times 12 \times 1 \right) D \text{ units} \]

\[ \text{Contribution of E} = 12D \text{ units} \]

Determining the Contribution Ratio

Finally, we need to find the ratio of M's contribution to E's contribution. The ratio is expressed as \(\text{Contribution of M : Contribution of E}\).

\[ \text{Ratio} = 6D : 12D \]

To simplify the ratio, we can divide both sides by \(6D\):

\[ \text{Ratio} = \frac{6D}{6D} : \frac{12D}{6D} \]

\[ \text{Ratio} = 1 : 2 \]

Therefore, the ratio of contribution of M to contribution of E in the project is 1:2.

This type of problem tests your understanding of work, efficiency, and time concepts in a combined manner, often seen in quantitative aptitude sections of various examinations.