If 10 boys and 12 girls together complete a work In 10 days while 8 boys and 12 girls together can work in 12 days one boy's work is equal to the work of how many girls ?

Options

A. 4
B. 5
C. 6
D. 7

Answer

To solve the problem step by step, we need to find out how much work one boy can do in comparison to girls. Let's break it down:

### Step 1: Establish the work done by boys and girls
Let the work done by one boy in one day be \( B \) and the work done by one girl in one day be \( G \).

### Step 2: Set up equations based on the information given
From the problem, we have two scenarios:

1. **10 boys and 12 girls complete the work in 10 days:**
\[ (10B + 12G) \times 10 = W \quad \text{(where W is the total work)} \]
Simplifying this gives:
\[ 10B + 12G = \frac{W}{10} \]

2. **8 boys and 12 girls complete the work in 12 days:**
\[ (8B + 12G) \times 12 = W \]
Simplifying this gives:
\[ 8B + 12G = \frac{W}{12} \]

### Step 3: Equate the total work
Since both expressions equal \( W \), we can set them equal to each other:
\[ 10(10B + 12G) = 12(8B + 12G) \]

### Step 4: Expand and simplify the equation
Expanding both sides:
\[ 100B + 120G = 96B + 144G \]

### Step 5: Rearrange the equation
Now, rearranging gives:
\[ 100B - 96B = 144G - 120G \]
This simplifies to:
\[ 4B = 24G \]

### Step 6: Solve for the relationship between boys and girls
Dividing both sides by 4:
\[ B = 6G \]

### Conclusion
This means that the work done by one boy is equal to the work done by 6 girls.

### Final Answer
1 boy's work is equal to the work of 6 girls.

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