Water is distributed to a town of 50000 inhabitants from a rectangular reservoir consisting of three equal compartments. Each compartment has a length and breadth 200 m and 100 m respectively, and 12 m depth of water in the beginning. The allowance is 20 litres per head per day. For how many days will the supply of water hold out?

Options

A. 240 days
B. 720 days
C. 800 days
D. 900 days

Answer

To solve the problem step by step, we will calculate the total volume of water in the reservoir, the daily water requirement for the town, and then determine how many days the water supply will last.

### Step 1: Calculate the volume of one compartment
The volume \( V \) of a rectangular compartment can be calculated using the formula:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
Given:
- Length = 200 m
- Breadth = 100 m
- Depth (Height) = 12 m

Substituting the values:
\[ V = 200 \, \text{m} \times 100 \, \text{m} \times 12 \, \text{m} = 240000 \, \text{m}^3 \]

### Step 2: Calculate the total volume of water in all compartments
Since there are three equal compartments, the total volume \( V_{\text{total}} \) is:
\[ V_{\text{total}} = 3 \times V = 3 \times 240000 \, \text{m}^3 = 720000 \, \text{m}^3 \]

### Step 3: Convert the total volume from cubic meters to liters
1 cubic meter is equivalent to 1000 liters. Therefore, the total volume in liters is:
\[ V_{\text{total}} = 720000 \, \text{m}^3 \times 1000 \, \text{liters/m}^3 = 720000000 \, \text{liters} \]

### Step 4: Calculate the daily water requirement for the town
The town has 50,000 inhabitants, and each person requires 20 liters of water per day. The total daily water requirement \( R \) is:
\[ R = \text{Number of inhabitants} \times \text{Water allowance per head} \]
Substituting the values:
\[ R = 50000 \times 20 \, \text{liters} = 1000000 \, \text{liters/day} \]

### Step 5: Calculate the number of days the water supply will last
To find the number of days \( D \) the water supply will last, we divide the total volume of water by the daily requirement:
\[ D = \frac{V_{\text{total}}}{R} = \frac{720000000 \, \text{liters}}{1000000 \, \text{liters/day}} = 720 \, \text{days} \]

### Final Answer
The supply of water will hold out for **720 days**.

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