Twenty men can complete a piece of work in 18 days, while eighteen women can complete the same work in 15 days. What is the ratio between the working capacity per day of a woman and that of a man?

Introduction / Context:
This question tests your understanding of work rate comparison between two different types of workers, here men and women. Instead of asking for the total time to complete a job, the problem asks for the ratio of the capacities of individual workers. Such questions are very important in aptitude exams because they check whether you can convert group work information into per person efficiencies and then compare them properly.

Given Data / Assumptions:

• Twenty men can complete the work in 18 days.
• Eighteen women can complete the same work in 15 days.
• All men have equal efficiency and all women have equal efficiency.
• The total work is the same in both situations.
• We need the ratio: (work done by one woman in one day) : (work done by one man in one day).

Concept / Approach:
Use the basic work formula: Work = Rate * Time. If a group completes a job, the total work can be expressed as (number of workers * individual rate * time). Since both groups complete the same work, we can equate the total work in man units and woman units and compare their individual rates. The unknowns here are the daily work rates of one man and one woman, but only the ratio is needed, which simplifies the calculation.

Step-by-Step Solution:
Let the work done by one man per day be m units. Let the work done by one woman per day be w units. Total work using men: 20 men * 18 days * m = 360m units. Total work using women: 18 women * 15 days * w = 270w units. Since both complete the same work, 360m = 270w. So, w / m = 360 / 270. Simplify: 360 / 270 = 36 / 27 = 4 / 3. Therefore, the ratio woman : man = 4 : 3.

Verification / Alternative check:
If you assume a convenient total work value, for example 360 units, then one man's rate becomes 360 / (20 * 18) = 1 unit per day, and one woman's rate becomes 360 / (18 * 15) = 4 / 3 units per day. This again gives the ratio woman : man = 4 : 3, confirming the previous result.

Why Other Options Are Wrong:
Ratios such as 3:4, 5:4 and 2:3 arise if you incorrectly invert the ratio or mix up the roles of men and women when equating the work. These options represent common handling mistakes in algebra or simplification but do not satisfy the equation 360m = 270w with correct orientation for woman : man.

Common Pitfalls:
Students sometimes compare total days directly rather than total work. Another frequent error is to compute m / w instead of w / m and then forget to invert the ratio. Careful interpretation of “capacity of a woman to that of a man” is essential: it clearly asks for woman : man, not man : woman.

Final Answer:
The ratio of the working capacity of a woman to that of a man is 4 : 3.