Question

Colonel, Major and General started a work together for Rs. 816. Colonel and Major did \(\frac{8}{17}\) of the total work, while Major and General together did \(\frac{12}{17}\) of the whole work. What is the amount of the least efficient person? (a) Rs. 256 (b) Rs. 144 (c) Rs. 85 (d) can't be determined.

Short answer

Answer: (d) can't be determined

Step-by-step solution

Calculate the remaining work done by General alone.

We know that Colonel and Major did \(\frac{8}{17}\) and Major and General did \(\frac{12}{17}\) of the work. We can find the remaining work done by General alone by subtracting the work done by Colonel and Major from the work done by Major and General: Remaining work = Work done by Major and General - Work done by Colonel and Major Remaining work = \(\frac{12}{17} - \frac{8}{17}\) Remaining work = \(\frac{4}{17}\)

Calculate the work done by Colonel and Major separately.

Now, we have the total work done by all three individuals. We know that of this total work, \(\frac{4}{17}\) was done by General alone. So, the remaining \(\frac{13}{17}\) work is done by Colonel and Major together. We can calculate the work done by each Colonel and Major individually as: Work done by Colonel + Work done by Major = \(\frac{13}{17}\) Since we know that Colonel and Major did the work together and both equally contributed, we can assume their work contribution to be the same: Work done by Colonel = Work done by Major = half of \(\frac{13}{17}\) Work done by Colonel = Work done by Major = \(\frac{1}{2} \cdot \frac{13}{17}\) Work done by Colonel = Work done by Major = \(\frac{13}{34}\)

Calculate the amount corresponding to the work done by each individual.

Now that we have the respective work contribution of each individual, we can calculate the amount earned by each individual: Total amount = Rs. 816 Amount earned by Colonel = \(\frac{13}{34}\) * Rs. 816 Amount earned by Major = \(\frac{13}{34}\) * Rs. 816 Amount earned by General = \(\frac{4}{17}\) * Rs. 816 Calculating the amounts, we get: Amount earned by Colonel = Rs. 312 Amount earned by Major = Rs. 312 Amount earned by General = Rs. 192

Determine the least efficient person and their amount.

The smallest amount earned is Rs. 192, which is earned by General. Thus, the least efficient person is General. So the amount of the least efficient person (General) is Rs. 192. The correct answer is not among the choices given, so the answer should be (d) can't be determined.

Key concepts

Efficiency Calculation

Efficiency is a measure of how much work someone can accomplish over a certain period of time. Understanding efficiency is important when evaluating individuals working together to complete a task. Here, efficiency reflects the total amount of work done by each participant in a group task.To calculate efficiency, break down the problem into manageable parts:

• Identify the total work completed.
• Determine the contribution of each participant.
• Calculate the fraction of the total work completed by each individual.

In this problem, by identifying the part of the work each person completes, we can determine efficiency. General completed \( \frac{4}{17} \) of the work independently. Colonel and Major, working together, completed \( \frac{13}{17} \). Thus, General is deemed the least efficient person based on the smallest fraction of work completed.

Proportion of Work

The proportion of work relates to how much each person contributes to a task. It illustrates how effort and time are distributed among team members. Proportion is often expressed as a fraction or percentage of the total work.In our exercise, different fractions represent the proportion of work:

• Colonel and Major combined: \( \frac{8}{17} \)
• Major and General combined: \( \frac{12}{17} \)
• General alone: \( \frac{4}{17} \)

These proportions tell us how much work each group or individual completed. Understanding these proportions helps see the bigger picture of work distribution within a team.

Problem-Solving Steps

Following a clear sequence of steps is essential for solving problems effectively. Breaking down problems into smaller steps encourages logical thinking and simplifies complex tasks. Here's a step-by-step guide used in this example:

• Identify known quantities: Start with fractions of work done.
• Calculate unknown variables: Work remaining by each individual.
• Use subtraction to find individual contributions.
• Convert work completed into monetary amounts.
• Determine which person did the least work.

These steps helped to identify General as the least efficient person due to the smallest work contribution.

Income Distribution

Income distribution is about sharing earnings based on work accomplishments. It illustrates the relationship between work done and rewards received. In team settings, recognizing individuals' contributions maintains fairness and motivation. For our specific scenario:

• Total earning: Rs. 816
• Colonel: Rs. 312
• Major: Rs. 312
• General: Rs. 192

By distributing income according to the portion of work completed, it ensures equitable compensation. The challenge lies in aligning earnings with efficiency, which in our case, shows General received the least due to the smaller workload completed.