50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m³, then the rise in the water level in the tank will be :

### Concept & Volume Displacement According to Archimedes' principle (in a simplified geometric context), the total volume of water displaced directly correlates to the rise in the water level spread across the surface area of the tank. $$ Rise in Level = \frac{Total Volume Displaced}{Surface Area of Tank Base} $$ ### Step-by-Step Solution 1. **Calculate Total Volume Displaced**: - Volume displaced by 1 man = 4 m³ - Volume displaced by 50 men = $50 \times 4 = 200$ m³ 2. **Calculate Base Area of the Tank**: - Area = Length × Breadth = $40 \text{ m} \times 20 \text{ m} = 800$ m² 3. **Calculate the Rise in Water Level**: - Rise ($H$) = Volume / Area - Rise = $200 / 800 = \frac{1}{4}$ meter = 0.25 m 4. **Convert Units**: - The options are in centimeters. - $0.25 \text{ m} \times 100 \text{ cm/m} = 25$ cm. ### Exam Strategy & Shortcut Since total displacement is $200$, and the area is $800$, the fraction is obviously $\frac{1}{4}$. Knowing instantly that $\frac{1}{4}$ of a meter is 25 cm allows you to solve this entirely in your head within 10 seconds. ### Common Pitfall Forgetting to convert the final answer from meters to centimeters. If you stop at 0.25, you won't find it in the options and might start over unnecessarily. ### Final Answer Therefore, the correct answer is **25 cm**.