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?

### Concept & Proportional Output When the time (days) remains constant, the work done (mats made) is directly proportional to the total effective workforce. We convert the mixed group into a single unit to see how it compares to the original group. $$ \text{Work} \propto \text{Workforce} $$ ### Step-by-Step Solution * First, establish the equivalency from the "or" statement: $10 \text{ men} = 20 \text{ boys}$. * Simplify this ratio: $1 \text{ man} = 2 \text{ boys}$. * Evaluate the target group: 8 men and 4 boys. * Convert the boys to men to match our primary unit: Since $2 \text{ boys} = 1 \text{ man}$, then $4 \text{ boys} = 2 \text{ men}$. * Find the total equivalent workforce of the new group: $8 \text{ men} + 2 \text{ men} = 10 \text{ men}$. * The new workforce is exactly 10 men. * From the initial conditions, we know that 10 men make 260 mats in 20 days. * Since the new group is mathematically equivalent to 10 men, and they are also working for 20 days, they will produce the exact same amount of work. * Mats made = 260. ### Exam Strategy & Shortcut Always calculate the total equivalent workforce *first* before plugging numbers into complex chain rule formulas. Here, a quick mental check ($4 \text{ boys} = 2 \text{ men} \rightarrow 8+2 = 10 \text{ men}$) reveals the workforce is identical to the given scenario. No calculation is needed; the output is identical. ### Common Pitfall Blindly using the formula $\frac{M_1 D_1}{W_1} = \frac{M_2 D_2}{W_2}$ without checking if $M_1$ and $M_2$ are actually the same. While the formula will yield the correct answer, it consumes precious time that could be saved through simple observation. ### Final Answer Therefore, the correct answer is **260**.