The problem states:

A tank contains $18 \frac{3}{7}$ liters of water. Due to leakage, $\frac{3}{5}$ of the water gets wasted. How much water is available for consumption?

Step-by-Step Solution:

1. Convert the mixed fraction $18 \frac{3}{7}$ into an improper fraction: $18 \frac{3}{7} = \frac{(18 \times 7) + 3}{7} = \frac{126 + 3}{7} = \frac{129}{7}$ So, the total water in the tank is $\frac{129}{7}$ liters.

2. The amount of water wasted is $\frac{3}{5}$ of the total water. To find how much water is wasted, multiply the total water by $\frac{3}{5}$: $\text{Water wasted} = \frac{3}{5} \times \frac{129}{7} = \frac{3 \times 129}{5 \times 7} = \frac{387}{35} \, \text{liters}$

3. Now, subtract the water wasted from the total water to find how much is left for consumption: $\text{Water left} = \frac{129}{7} - \frac{387}{35}$ First, convert the fractions to have the same denominator. The least common denominator (LCD) of 7 and 35 is 35: $\frac{129}{7} = \frac{129 \times 5}{7 \times 5} = \frac{645}{35}$ Now, subtract the two fractions: $\text{Water left} = \frac{645}{35} - \frac{387}{35} = \frac{645 - 387}{35} = \frac{258}{35} \, \text{liters}$

4. Simplify $\frac{258}{35}$. This cannot be simplified further, so the final answer is: $\text{Water left for consumption} = \frac{258}{35} \approx 7.37 \, \text{liters}$

Final Answer:

The amount of water available for consumption is approximately 7.37 liters.

Do you want more details or have any questions?

Here are 5 related questions:

1. How do you convert a mixed fraction into an improper fraction?
2. What is the process for multiplying fractions?
3. How can you find the least common denominator for two fractions?
4. How do you subtract two fractions with different denominators?
5. What is the real-life significance of understanding percentages in problems like leakage?

Tip: When dealing with fractional quantities, always ensure the denominators are the same before performing addition or subtraction.