If 10 men can do a work in 6 days and 15 women can do the same in 5 days, Then 8 men and 5 women can together do the work in :

Appeared in: NHM MP Staff Nurse-2022

Explanation

The work rate of one man is calculated as 1/60 of the work per day (since 10 men take 6 days, total work is 60 man-days).
The work rate of one woman is calculated as 1/75 of the work per day (since 15 women take 5 days, total work is 75 woman-days).
The combined daily work of 8 men and 5 women is the sum of their individual contributions: (8 × 1/60) + (5 × 1/75).
This simplifies to 2/15 + 1/15 = 3/15 = 1/5 of the work per day.
If 1/5 of the work is done each day, the total work will be completed in 5 days.

Option A: 7 days is incorrect. This would imply a daily work rate of 1/7, which is slower than the calculated combined rate of 1/5. This answer might arise from a miscalculation of the combined work rate.
Option B: 6 days is incorrect. This is the time it takes for 10 men alone to do the work. It fails to account for the additional work contributed by the 5 women, which would reduce the total time taken.
Option D: 4 days is incorrect. This would imply a daily work rate of 1/4, which is faster than the calculated combined rate of 1/5. This answer might result from an arithmetic error that overestimates the group's efficiency.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating combined work rates in Time and Work problems as background academic context rather than a clinical decision trigger.
This question tests quantitative aptitude and logical reasoning, which are essential components of general intelligence sections in nursing entrance exams.
Strong problem-solving skills are crucial for nurses in clinical settings for tasks like medication dosage calculations, fluid intake/output monitoring, and resource management.
What if the question asked for the work done by 8 men and 5 women in 2 days? The answer would be 2 * (1/5) = 2/5 of the total work.

How to Approach the Question

First, identify the initial conditions: 10 men take 6 days, and 15 women take 5 days.
Calculate the total amount of work in 'man-days' (10 * 6 = 60) and 'woman-days' (15 * 5 = 75).
From this, determine the work rate of a single individual per day. One man does 1/60 of the work per day, and one woman does 1/75 of the work per day.
Calculate the combined daily work rate for the new group specified in the question (8 men and 5 women) by summing their individual rates: (8 * 1/60) + (5 * 1/75).
Simplify the expression to find the fraction of work done per day.
The total time required to complete the work is the reciprocal of this combined daily work rate.

Concept Tested & Keywords

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