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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.

Please read the question carefully and answer the questions carefully

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

OPTIONS

3 : 8

5 : 7

6 : 7

None

Let's calculate the ratio of the working efficiency of a woman to that of a boy.

### Step 1: Determine the total work done in terms of man-hours, woman-hours, and boy-hours.

#### For the men:
- 20 men complete the work in 10 days, working 5 hours a day.
- Total work = \( 20 \times 10 \times 5 = 1000 \) man-hours.

#### For the women:
- 30 women complete the work in 20 days, working 8 hours a day.
- Total work = \( 30 \times 20 \times 8 = 4800 \) woman-hours.

#### For the boys:
- 30 boys complete the work in 15 days, working 4 hours a day.
- Total work = \( 30 \times 15 \times 4 = 1800 \) boy-hours.

### Step 2: Compare the efficiency of women and boys.
- Let the efficiency of a man be \( M \), a woman be \( W \), and a boy be \( B \).
- Given the same amount of work is done, we have:

\[ 1000M = 4800W = 1800B \]

### Step 3: Calculate the ratio of efficiency \( W/B \).
- From \( 1000M = 4800W \), \( M = 4.8W \).
- From \( 1000M = 1800B \), \( M = 1.8B \).

Thus, we equate the two:

\[ 4.8W = 1.8B \]

\[ \frac{W}{B} = \frac{1.8}{4.8} \]

Simplifying the ratio:

\[ \frac{W}{B} = \frac{3}{8} \]

### Answer:

The ratio of the working efficiency of a woman to that of a boy is **3 : 8**.

The correct option is **3 : 8**.

Would you like more details on this solution or have any other questions?

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Here are five questions you might find interesting:

1. What would be the efficiency ratio of a man to a woman?
2. If 10 men and 15 women work together, how long would it take them to complete the work?
3. How does the total work in man-hours compare with the work in boy-hours?
4. What would happen to the efficiency ratio if the number of working days for boys was reduced by 5?
5. How would the result change if the number of hours women worked per day increased to 10?

**Tip:** Always break down work-related problems into smaller parts to identify the relationship between different variables, such as work done per person or time required.

20 men complete a work in 10 days working 5 hours a day, 30 women complete a work in 20 days working 8 hours a day, and 30 boys complete a work in 15 days working 4 hours a day. What is the ratio of the working efficiency of a woman to that of a boy?

This problem explores the calculation of the efficiency ratio between women and boys in a work and time scenario. Learn how to determine the total work done and compare the efficiency of different groups. Suitable for students in Grades 8-10.

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