A man can do a work in 20 days and a woman can do the same work in 30 days. In how many days will 2 men and 3 women do the work?

Appeared in: PGIMER Chandigarh NO - 2015

Explanation

The fundamental principle is to convert the time taken by each person into their 'work rate' per day.
One man's 1-day work is 1/20. Therefore, two men's 1-day work is 2 * (1/20) = 1/10.
One woman's 1-day work is 1/30. Therefore, three women's 1-day work is 3 * (1/30) = 1/10.
The combined work rate of 2 men and 3 women is the sum of their individual rates: 1/10 + 1/10 = 2/10 = 1/5 of the work per day.
If 1/5 of the work is done in one day, the total time to complete the work is the reciprocal of the rate, which is 5 days.

Option A: This result is incorrect. It might arise from a miscalculation, such as incorrectly adding or manipulating the fractions representing the work rates.
Option C: This is an incorrect calculation. It does not follow the correct method of combining work rates. A possible error could be averaging the times or another logical fallacy.
Option D: This result is incorrect. It likely stems from an error in calculating the combined work rate or in finding the reciprocal to determine the total time.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the concept of 'Time and Work' from quantitative aptitude, which involves calculating the efficiency or rate of work of individuals and combining them to find the total time taken to complete a task as background academic context rather than a clinical decision trigger.
This question assesses basic numeracy and problem-solving skills, which are foundational for various calculations in nursing.
Nurses frequently use similar logical and mathematical skills for tasks like medication dosage calculations, fluid balance monitoring, and interpreting patient data, where precision is critical for patient safety.
What if? - If the question asked for 3 men and 2 women, the calculation would change. 3 men's work = 3/20. 2 women's work = 2/30 = 1/15. Combined work = 3/20 + 1/15 = (9+4)/60 = 13/60. Total time would be 60/13 days, or approximately 4.6 days.

How to Approach the Question

First, identify the time each individual takes to complete the work alone. Here, it's 20 days for a man and 30 days for a woman.
Calculate the rate of work for one individual per day. The rate is the reciprocal of the time taken (Rate = 1/Time). So, a man's rate is 1/20 and a woman's rate is 1/30.
Determine the total rate of work for the group mentioned in the question (2 men and 3 women). Multiply the individual rates by the number of people: (2 * 1/20) + (3 * 1/30).
Simplify the expression: 1/10 + 1/10 = 2/10 = 1/5. This is the fraction of the work the group completes in one day.
To find the total number of days to complete the entire work, take the reciprocal of the combined daily work rate: 1 / (1/5) = 5.
Select the option that matches your calculated result.

Concept Tested & Keywords

Concept Tested: This question tests the concept of 'Time and Work' from quantitative aptitude, which involves calculating the efficiency or rate of work of individuals and combining them to find the total time taken to complete a task.
Stem keywords: man, woman, work, days
Lead-in keywords: In how many days

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