If 10 men or 20 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 4 boys in 20 days?

Options

A. 260
B. 240
C. 280
D. 520

Answer

To solve the problem step by step, we need to find out how many mats can be made by 8 men and 4 boys in 20 days, given that 10 men or 20 boys can make 260 mats in 20 days.

### Step 1: Determine the work done by 1 man and 1 boy in 20 days.
From the problem, we know:
- 10 men can make 260 mats in 20 days.
- 20 boys can also make 260 mats in 20 days.

Let's first find out how many mats 1 man can make in 20 days:
- If 10 men make 260 mats, then 1 man makes:
\[ \text{Mats made by 1 man} = \frac{260 \text{ mats}}{10 \text{ men}} = 26 \text{ mats} \]

Now, let's find out how many mats 1 boy can make in 20 days:
- If 20 boys make 260 mats, then 1 boy makes:
\[ \text{Mats made by 1 boy} = \frac{260 \text{ mats}}{20 \text{ boys}} = 13 \text{ mats} \]

### Step 2: Calculate the total work done by 8 men and 4 boys in 20 days.
Now, we can calculate how many mats can be made by 8 men and 4 boys in 20 days:
- Mats made by 8 men:
\[ \text{Mats by 8 men} = 8 \text{ men} \times 26 \text{ mats/man} = 208 \text{ mats} \]

- Mats made by 4 boys:
\[ \text{Mats by 4 boys} = 4 \text{ boys} \times 13 \text{ mats/boy} = 52 \text{ mats} \]

### Step 3: Add the total mats made by both men and boys.
Now, we add the mats made by men and boys to get the total:
\[ \text{Total mats} = \text{Mats by 8 men} + \text{Mats by 4 boys} = 208 \text{ mats} + 52 \text{ mats} = 260 \text{ mats} \]

### Conclusion:
Thus, the total number of mats that will be made by 8 men and 4 boys in 20 days is **260 mats**.

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