Explanation:

Sol. Ans.(a).

Regular method: Let the weight of empty vessel = v and weight of water = w, then by the conditions given we have

v + w = 40 …. (1) and

v + w/3 = 20 …. (2)

By solving equations (1) and (2) simultaneously we have w = 30 and v = 10.

Short-cut: Taking option (a), weight of empty vessel = 10, so weight of water when vessel is completely filled = 40 – 10 = 30. When water is one-third fill its weight = 30/3 = 10. So weight of vessel when one-third filled with water = 10 + 10 = 20. Which matches with the condition given in question. So answer is option (a).