If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys to do the same type of work will be :

Answer

To solve the problem, we need to find out how long it will take for 15 men and 20 boys to complete the same work given the work rates of men and boys from the previous information.

### Step-by-Step Solution:

1. **Determine the Work Done by 6 Men and 8 Boys in 10 Days:**
- Let the work done by 1 man in 1 day be \( M \) units.
- Let the work done by 1 boy in 1 day be \( B \) units.
- Therefore, the total work done by 6 men and 8 boys in 10 days can be expressed as:
\[ (6M + 8B) \times 10 = 60M + 80B \]

2. **Determine the Work Done by 26 Men and 48 Boys in 2 Days:**
- Similarly, the total work done by 26 men and 48 boys in 2 days is:
\[ (26M + 48B) \times 2 = 52M + 96B \]

3. **Set the Two Work Equations Equal:**
- Since both expressions represent the same total work, we can set them equal to each other:
\[ 60M + 80B = 52M + 96B \]

4. **Rearrange the Equation:**
- Rearranging gives:
\[ 60M - 52M = 96B - 80B \]
\[ 8M = 16B \]
- Simplifying this gives:
\[ M = 2B \]

5. **Calculate Total Work in Terms of Units:**
- Now, substitute \( M \) in terms of \( B \) back into the first equation to find the total work:
\[ 60M + 80B = 60(2B) + 80B = 120B + 80B = 200B \]
- Thus, the total work is \( 200B \) units.

6. **Determine the Work Done by 15 Men and 20 Boys:**
- Now we calculate the work done by 15 men and 20 boys:
\[ \text{Work done by 15 men} = 15M = 15(2B) = 30B \]
\[ \text{Work done by 20 boys} = 20B \]
- Therefore, the total work done by 15 men and 20 boys in one day is:
\[ 30B + 20B = 50B \]

7. **Calculate the Time Taken to Complete the Work:**
- To find the time taken to complete \( 200B \) units of work at a rate of \( 50B \) units per day:
\[ \text{Time} = \frac{\text{Total Work}}{\text{Work per Day}} = \frac{200B}{50B} = 4 \text{ days} \]

### Final Answer:
The time taken by 15 men and 20 boys to complete the work is **4 days**.

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