12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required, is:

### Concept & Work Equivalence Formula When the total amount of work is constant, the product of the number of men ($M$), days ($D$), and hours per day ($H$) remains constant. $$ M_1 \times D_1 \times H_1 = M_2 \times D_2 \times H_2 $$ ### Step-by-Step Solution * **Given**: - Scenario 1: $M_1 = 12$, $H_1 = 8$, $D_1 = 10$ - Scenario 2: $D_2 = 8$, $H_2 = 15$, $M_2 = x$ * **Calculation**: $$ 12 \times 8 \times 10 = x \times 8 \times 15 $$ $$ 960 = 120x $$ $$ x = \frac{960}{120} = 8 $$ ### Exam Strategy & Shortcut Cancel common terms on both sides before multiplying. Notice that $8$ appears on both sides of the equation ($12 \times 8 \times 10 = x \times 8 \times 15$), which simplifies to $12 \times 10 = 15x$, yielding $x = \frac{120}{15} = 8$. ### Common Pitfall Forgetting to account for either the hours or days change, or incorrectly setting up the inverse relationships as direct ratios. ### Final Answer Therefore, the correct answer is **8**.