A water tank is initially 2/5 full of water. When 16 litres of water are added to the tank, the level rises so that it becomes 6/7 full of its total capacity. What is the full capacity of the water tank, in litres?

Introduction / Context:
This aptitude question tests your understanding of fractions, linear equations, and the idea of comparing two different fill levels of the same water tank. Problems like this appear frequently in bank exams, placement tests, and general competitive exams because they check whether you can translate a word problem into a simple algebraic equation. The key idea is that the capacity of the tank remains fixed, while the amount of water inside changes when more water is added. By carefully relating the fractional levels of 2/5 and 6/7 and the added 16 litres, we can determine the full capacity of the tank.

Given Data / Assumptions:

• The water tank is initially 2/5 full.
• After adding 16 litres of water, the tank becomes 6/7 full.
• The capacity of the tank is the same in both situations.
• We assume no leakage or loss of water.

Concept / Approach:
The concept used is simple linear algebra based on fractions of the same whole. Let the full capacity of the tank be C litres. Initially the volume of water is (2/5) * C. After adding 16 litres, the volume becomes (6/7) * C. Since the only change between the two situations is the addition of 16 litres, the difference between the later amount and the initial amount must be exactly 16 litres. This gives us a single linear equation in the unknown C, which can then be solved easily.

Step-by-Step Solution:
Let the full capacity of the tank be C litres. Initial quantity of water = (2/5) * C litres. Final quantity of water after adding 16 litres = (6/7) * C litres. According to the problem, initial quantity + 16 = final quantity. So, (2/5) * C + 16 = (6/7) * C. Bring the fractional terms to one side: 16 = (6/7) * C - (2/5) * C. Compute the difference using a common denominator of 35: (6/7) * C = (30/35) * C and (2/5) * C = (14/35) * C. Therefore, (6/7) * C - (2/5) * C = (30/35 - 14/35) * C = (16/35) * C. So, 16 = (16/35) * C. Solve for C by multiplying both sides by 35 and dividing by 16. C = 16 * 35 / 16 = 35 litres.

Verification / Alternative check:
We can quickly check the result by substituting C = 35 litres back into the original conditions. Initially, the tank has (2/5) * 35 = 14 litres of water. After adding 16 litres, the volume becomes 14 + 16 = 30 litres. Now calculate 6/7 of the full capacity: (6/7) * 35 = 30 litres. Since the final amount of water matches 6/7 of the capacity exactly, the value C = 35 litres is fully consistent with the given data, confirming that the calculation is correct.

Why Other Options Are Wrong:
28 litres: For capacity 28 litres, 2/5 of 28 is 11.2 litres, and adding 16 gives 27.2 litres, which is not 6/7 of 28 (which is 24 litres).
32 litres: For capacity 32 litres, 2/5 of 32 is 12.8 litres. Adding 16 gives 28.8 litres, while 6/7 of 32 is 27.428571 litres, so it does not match.
42 litres: For capacity 42 litres, 2/5 of 42 is 16.8 litres, and adding 16 gives 32.8 litres, but 6/7 of 42 is 36 litres, so this is also inconsistent.
30 litres: For capacity 30 litres, 2/5 of 30 is 12 litres, and adding 16 gives 28 litres, whereas 6/7 of 30 is 25.714285 litres, so this option fails too.

Common Pitfalls:
Many learners mistakenly set up the equation using 2/5 of the difference between levels instead of applying the fractions to the full capacity. Another common mistake is to treat the denominators 5 and 7 casually and introduce arithmetic errors when finding a common denominator. Some students also incorrectly add fractions of different denominators directly without converting them to a common base. Careful algebraic manipulation and checking the equation after writing it are essential to avoid these errors.

Final Answer:
Thus, the full capacity of the water tank is 35 litres.