A tank is 2/5 part full. If 16 litres of water is added to the tank, it becomes 6/7 part full, then total capacity of tank is :

Question

Accepted Answer

To determine the total capacity of the tank, we need to analyze the information given in the problem and use logical reasoning to support Option 2 as the correct answer.

1. **Understanding the Problem:**
   - Initially, the tank is 2/5 full.
   - After adding 16 liters of water, the tank becomes 6/7 full.

2. **Setting Up the Equation:**
   - Let the total capacity of the tank be $ x $ liters.
   - Initially, the tank has $ \frac{2}{5}x $ liters of water.
   - After adding 16 liters, the tank has $ \frac{6}{7}x $ liters of water.

3. **Formulating the Equation:**
   - The equation based on the above information is:
     $$
     \frac{2}{5}x + 16 = \frac{6}{7}x
     $$

4. **Solving the Equation:**
   - Rearrange the equation to isolate $ x $:
     $$
     16 = \frac{6}{7}x - \frac{2}{5}x
     $$
   - Find a common denominator for the fractions:
     $$
     16 = \left(\frac{30}{35}x - \frac{14}{35}x\right)
     $$
   - Simplify the equation:
     $$
     16 = \frac{16}{35}x
     $$
   - Solve for $ x $:
     $$
     x = 16 \times \frac{35}{16} = 35
     $$

5. **Conclusion:**
   - The total capacity of the tank is 35 liters, which corresponds to Option 2.

6. **Explanation of Incorrect Options:**
   - **Option 1 (24 liters):** If the total capacity were 24 liters, the initial amount of water would be $ \frac{2}{5} \times 24 = 9.6 $ liters. Adding 16 liters would result in 25.6 liters, which is not $ \frac{6}{7} \times 24 = 20.57 $ liters.
   - **Option 3 (38 liters):** If the total capacity were 38 liters, the initial amount of water would be $ \frac{2}{5} \times 38 = 15.2 $ liters. Adding 16 liters would result in 31.2 liters, which is not $ \frac{6}{7} \times 38 = 32.57 $ liters.
   - **Option 4 (42 liters):** If the total capacity were 42 liters, the initial amount of water would be $ \frac{2}{5} \times 42 = 16.8 $ liters. Adding 16 liters would result in 32.8 liters, which is not $ \frac{6}{7} \times 42 = 36 $ liters.

Therefore, the only option that satisfies the conditions of the problem is Option 2, which is 35 liters.