Question

Abhishek can do a piece of work in 40 days. He alone worked at it for 8 days and then Bacchhan completed alone the rest work in 24 days. In how many days they will complete the whole work, working together? (a) \(17 \frac{1}{7}\) days (b) \(18 \frac{1}{7}\) days (c) \(9 \frac{1}{6}\) days (d) 14 days

Short answer

(a) 17 1/7 days (b) 24 days (c) 18 days (d) 20 days Answer: (a) 17 1/7 days

Step-by-step solution

Find the work done by Abhishek in a day

We are given that Abhishek can complete the work in 40 days. So, we can find his work done per day by dividing the total work by the number of days. Let the total work be represented by W. Then, Abhishek's work per day is: \(\frac{W}{40}\).

Calculate the work done by Bacchhan in a day

Since Abhishek worked for 8 days and Bacchhan completed the remaining work in 24 days, we can find the remaining work done by Bacchhan by subtraction. The work left for Bacchhan after Abhishek worked for 8 days is: \(W - 8(\frac{W}{40}) = W(1 - \frac{8}{40}) = W(\frac{32}{40}) = \frac{4W}{5}\) Now, since Bacchhan completed this remaining work in 24 days, we have: \(\frac{4W}{5} = 24 \times \text{Bacchhan's work per day}\) So, Bacchhan's work per day is: \(\text{Bacchhan's work per day} = \frac{4W}{5 \times 24}\)

Calculate their combined work done in a day

Now, let's add their individual work done in a day to calculate their combined work done in a day: \(\text{Total work per day} = \frac{W}{40} + \frac{4W}{5 \times 24}\)

Find the number of days they need to complete the work together

Finally, we need to find out the number of days they will take working together to complete the work. To do this, we can divide the total work, W by their combined work done in a day: \(\text{Total days working together} = \frac{W}{(\frac{W}{40} + \frac{4W}{5 \times 24})}\) Simplifying, we get: \(\text{Total days working together} = \frac{W}{(\frac{W}{40} + \frac{W}{30})}\) Now, finding the Lowest Common Multiple (LCM) of 40 and 30, which is 120, we get: \(\text{Total days working together} = \frac{W}{(\frac{3W}{120} + \frac{4W}{120})} = \frac{W}{\frac{7W}{120}}\) Cancelling out W and simplifying: \(\text{Total days working together} = \frac{120}{7}\) Thus, the number of days Abhishek and Bacchhan will take to complete the whole work together is \(17 \frac{1}{7}\) days. So, the answer is (a) \(17 \frac{1}{7}\) days.

Key concepts

Time Management

Time management is an essential skill not only in academics but also in everyday life. When faced with tasks, managing time efficiently can lead to impressive productivity. In the problem, Abhishek and Bacchhan demonstrate effective time management by planning their work schedules to complete a task together. Here's how good time management benefits such scenarios:

• **Scheduling**: By understanding how long each person takes individually, a proper schedule can be set, allowing tasks to be divided effectively.
• **Prioritization**: Determine which tasks should be tackled together or separately, allowing for simultaneous progression of the work.
• **Deadline Recognition**: Having a clear understanding of when tasks need to be completed encourages swiftness, preventing procrastination.

The practice of dividing the work based on time availability and constraints ensures that maximum productivity is achieved with the least amount of wasted time.

Work Efficiency

Work efficiency is about making the best use of resources to achieve a task with minimal waste of time and energy. The original problem showcases how evaluating an individual's work rate can lead to an understanding of efficiency.

• **Understanding Work Rates**: Calculating work done by Abhishek and Bacchhan per day gives an insight into their work efficiency.
• **Measuring Output**: By knowing outputs per day, you can determine who will need more support or who should take on more responsibility.
• **Resource Allocation**: Efficiently managing resources can also include human resources, like deciding how much of the problem Abhishek and Bacchhan take on.

Improving work efficiency involves evaluation, analysis, and strategic planning for better utilization of time and effort.

Collaboration in Work

Collaboration is a fundamental aspect when multiple individuals work together towards a common goal. In our case study, Abhishek and Bacchhan working collaboratively demonstrate several crucial elements of effective teamwork.

• **Complementary Skills**: Together, their abilities complement each other, as they manage to cut down the time taken to complete the task compared to working alone.
• **Communication**: Ensuring active and clear communication ensures that work continues smoothly with fewer delays or misunderstandings.
• **Shared Responsibility**: With shared responsibility, the workload is balanced, reducing stress and improving effectiveness.

Working together not only speeds up completion but also enhances the quality of work, as each can rely on the other’s strengths to cover their weaknesses.