A tank is 2/5 full. If 18 litres of water is added to the tank, it becomes 6/7 full. The capacity of the tank is:

Step 1: We know that the tank is 2/5 full before adding water and 6/7 full after adding water. So, the difference between 6/7 and 2/5 is the amount of water added.

Step 2: To find the difference, we need to convert the fractions to have a common denominator. The least common multiple of 7 and 5 is 35. So, we convert the fractions to have the denominator 35.

2/5 = 14/35 6/7 = 30/35

Step 3: Now, subtract 14/35 from 30/35 to find the amount of water added.

30/35 - 14/35 = 16/35

So, 16/35 of the tank's capacity is the amount of water added.

Step 4: We know that 16/35 of the tank's capacity is equal to 18 litres (from the problem statement). So, to find the full capacity of the tank, we set up the proportion:

16/35 = 18/x

Step 5: Solve for x (the full capacity of the tank) by cross-multiplying:

16x = 1835

Step 6: Divide both sides by 16 to solve for x:

x = (18*35) / 16

Step 7: Simplify to find the capacity of the tank:

x = 39.375 litres

So, the capacity of the tank is approximately 39.375 litres.