Water Supply Volume

The first step is to understand the total volume of water being treated per day. The question states that the city has a water supply of 15000 cubic meters per day.

Water supply volume = $15000 \text{ m}^3/\text{day}$

Chlorine Dosage and Requirement

The water is treated with a chlorine dosage of 0.5 ppm. ppm stands for parts per million, which can be interpreted as mg per liter for water treatment calculations. So, 0.5 ppm is equivalent to 0.5 mg of chlorine per liter of water.

We need to find the total amount of chlorine required per day. First, convert the water volume from cubic meters to liters:

• $1 \text{ m}^3 = 1000 \text{ liters}$
• Total water volume = $15000 \text{ m}^3/\text{day} \times 1000 \text{ L/m}^3 = 15,000,000 \text{ L/day}$

Now, calculate the total chlorine required per day based on the dosage:

• Chlorine required in mg/day = Dosage (mg/L) $\times$ Water Volume (L/day)
• Chlorine required = $0.5 \text{ mg/L} \times 15,000,000 \text{ L/day} = 7,500,000 \text{ mg/day}$

To convert milligrams to kilograms, we use the relationship $1 \text{ kg} = 1,000,000 \text{ mg}$.

• Chlorine required in kg/day = $7,500,000 \text{ mg} \times \frac{1 \text{ kg}}{1,000,000 \text{ mg}} = 7.5 \text{ kg/day}$

So, $7.5 \text{ kg}$ of pure chlorine is required per day.

Bleaching Powder Calculation

The question specifies that 25% bleaching powder is used. This means that for every 100 kg of bleaching powder, there are 25 kg of available chlorine. We need to find out how much 25% bleaching powder is required to provide $7.5 \text{ kg}$ of chlorine.

Let $X$ be the amount of 25% bleaching powder required in kg.

The amount of available chlorine in $X$ kg of bleaching powder is $25\%$ of $X$, which is $0.25 \times X$.

We need this amount of available chlorine to be equal to the required chlorine, which is $7.5 \text{ kg}$.

So, we can set up the equation:

$0.25 \times X = 7.5 \text{ kg}$

Now, solve for $X$:

$X = \frac{7.5 \text{ kg}}{0.25}$

$X = 30 \text{ kg}$

Therefore, $30 \text{ kg}$ of 25% bleaching powder is required per day.