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Directions: 20Men completes a work in 10days working 5 hours a day, 30 women completes a work in 20 days working 8 hours a day and 30 boys completes a work in 15 days working 4 hours a day.

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Please read the question carefully and answer the questions carefully

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What is the ratio of the working efficiency of Woman and boy

To find the ratio of the working efficiency of a woman to a boy, we will break the problem down step by step.

### Step 1: Determine the total work done by each group.

The total amount of work can be expressed in terms of "man-hours," "woman-hours," and "boy-hours," which represent the product of the number of workers, the number of days, and the number of hours worked each day.

#### For 20 men:
- 20 men work for 10 days, 5 hours each day.
- Total work done = \( 20 \times 10 \times 5 = 1000 \) man-hours.

#### For 30 women:
- 30 women work for 20 days, 8 hours each day.
- Total work done = \( 30 \times 20 \times 8 = 4800 \) woman-hours.

#### For 30 boys:
- 30 boys work for 15 days, 4 hours each day.
- Total work done = \( 30 \times 15 \times 4 = 1800 \) boy-hours.

### Step 2: Find the work done by one individual from each group.

We know that each group of workers is completing the same amount of work, so the total work is the same for men, women, and boys. Let’s assume the total work is \( W \). We can now express the work done by one person in each group.

- Work done by one man: \( \frac{W}{1000} \)
- Work done by one woman: \( \frac{W}{4800} \)
- Work done by one boy: \( \frac{W}{1800} \)

### Step 3: Calculate the efficiency ratio between a woman and a boy.

Efficiency is inversely proportional to the amount of time taken to complete the work. Therefore, the efficiency of one woman (relative to the work done by one person) can be compared to the efficiency of one boy.

- Efficiency of one woman: \( \frac{W}{4800} \)
- Efficiency of one boy: \( \frac{W}{1800} \)

Now, the ratio of the efficiency of a woman to a boy is:
\[
\text{Efficiency Ratio (Woman : Boy)} = \frac{1/4800}{1/1800} = \frac{1800}{4800} = \frac{3}{8}
\]

### Final Answer:
The ratio of the working efficiency of a woman to a boy is \( 3:8 \).

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Would you like further details or clarification?

Here are five related questions for practice:
1. What is the ratio of the working efficiency of a man to a woman?
2. If 10 women and 20 boys work together, how long will it take them to complete the same work?
3. How much more efficient is a man compared to a boy?
4. What is the total work done by 15 women working for 12 days at 6 hours per day?
5. If one man completes the work alone, how long would it take him?

**Tip:** Ratios are an easy way to compare relative efficiencies, but always remember to relate them to total work done.

Explore the ratio of working efficiency between women and boys in completing a work task based on given work rates and durations. Understand how to calculate efficiency ratios and apply them to similar problems.

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