A swimming bath is 24 m long and 15 m broad. When a number of men dive into the bath, the height of the water rises by 1 cm. If the average amount of water displaced by one of the men be 0.1 cu. m, how many men are there in the bath?

### Concept & Reverse Volume Displacement This is the inverse of a standard displacement problem. Here, you use the rise in water level to calculate the total displaced volume, and then divide by the displacement per person to find the number of people. $$ Total Displaced Volume = Base Area \times Rise in Height $$ $$ Number of People = \frac{Total Displaced Volume}{Volume Displaced per Person} $$ ### Step-by-Step Solution 1. **Standardize Units**: - Base Length = 24 m - Base Breadth = 15 m - Rise in Height = 1 cm = 0.01 m 2. **Calculate Total Displaced Volume**: - Total Volume = $24 \times 15 \times 0.01$ - Total Volume = $360 \times 0.01 = 3.6$ m³ 3. **Find the Number of Men**: - Average displacement per man = 0.1 m³ - Number of men = $3.6 / 0.1 = 36$ ### Exam Strategy & Shortcut Handle the multiplication quickly: $24 \times 15$ is just $24 \times \frac{30}{2} = 12 \times 30 = 360$. Multiplying by 0.01 shifts the decimal to 3.6. Dividing by 0.1 shifts it back to 36. ### Common Pitfall Using 1 for the height without converting cm to m. This would give a volume of 360 m³, resulting in 3600 men, which is physically impossible for that pool and missing from the options. Always check unit consistency. ### Final Answer Therefore, the correct answer is **36**.