Question

If 10 persons can do a job in 20 days, then 20 person wid twice the efficiency can do the same job in : (a) 5 days. (b) 40 days (c) 10 days (d) 20 days

Short answer

Answer: 5 days.

Step-by-step solution

Calculate the total work done by 10 persons in 20 days.

Let's denote the efficiency of one person as E. We know that 10 persons can do the job in 20 days. So, the total work done by them is: Work = 10 persons × E × 20 days (Using the Work formula)

Calculate the total work done by 20 persons with twice the efficiency.

Now, we know that 20 persons have twice the efficiency. So, the total work done by them will be: Work = 20 persons × 2E × Time (Using the Work formula)

Equate the total work in both cases and solve for Time.

Since the total work done in both cases is equal, we can set the expressions equal to each other: 10E × 20 days = 20 × 2E × Time Divide both sides by 20E: 20 days = 4 × Time Divide both sides by 4: Time = 5 days Therefore, the answer is (a) 5 days. 20 persons with twice the efficiency can complete the same job in 5 days.

Key concepts

Quantitative Aptitude

Quantitative aptitude is a measure of an individual's ability to perform numerical calculations swiftly and accurately. In the context of work and efficiency problems, like the textbook example provided, it involves understanding fundamental arithmetic operations, ratios, and algebraic expressions. To master these problems, one must be able to associate the given numerical data with the mathematical concepts that govern work, such as work done equals the number of workers multiplied by their efficiency and the time they spend working. The more you practice problems of this nature, the more intuitive these relationships will become, thereby enhancing your quantitative aptitude.

Man-Hours Concept

The man-hours concept is a crucial principle within the study of work and efficiency. Simply put, man-hours represent the amount of work that one individual can complete in one hour. It is a composite measure of the workforce size and the time attributed to the completion of a task. When solving problems based on this concept, as in our exercise, it is essential to understand that if the number of workers or their efficiency (or both) changes, the amount of time to complete the job will also vary. This is because the total man-hours remain consistent for a specific job; hence, increasing the number of workers or their efficiency naturally decreases the time required.

Rate of Work

The rate of work, often intertwined with the efficiency in work-related problems, refers to the speed at which a person or group of people can complete a task. It is commonly expressed as 'job per time unit'. For instance, if a person's rate of work is such that they can complete a job in 5 hours, another person with twice the rate of work can complete the same job in 2.5 hours. Understanding this will help in solving problems that involve variable work rates due to changes in efficiency or number of workers, just as illustrated in our exercise. By recognizing that a doubled work rate (or efficiency) would halve the time needed to finish a task, you can quickly solve these problems and arrive at the correct conclusion.