The story of why Gaṇeśa is offered dūrvā grass begins with a king who was very good at giving.
Janaka was famous for feeding people. He honoured brahmins, gave to those in need, and seemed to possess stores that never emptied. Nārada visited him and praised his generosity, but Janaka answered with words that made the problem clear: he spoke as though the giving, the wealth and the power behind it all belonged to him alone.
Nārada went to Gaṇeśa and told him what he had heard.
So Gaṇeśa took the appearance of an old, suffering brahmin guest and came to Janaka's door asking for food — not a little food, but enough to make him full.
Janaka welcomed him and ordered a meal.
The guest ate it.
More food came. He ate that too. The text says an amount sufficient for thousands disappeared, then plate after plate of good rice and porridge. Grain was gathered from stores, houses, the city and the villages. Everything brought before the guest was eaten, and he was still hungry.
At last Janaka's messengers had to tell the king that no grain could be found anywhere.
The guest left the palace and went from house to house asking for food. People could only tell him the same thing: the stores had already been emptied.
Then he reached a house with almost nothing in it.
A poor husband and wife lived there. When the guest entered, he found them worshipping an image of Gaṇeśa with fresh shoots and flowers. He told them that Janaka's abundance had not satisfied him and asked whether their house could give him anything.
They answered that they were poor and had no food. That morning they had gathered dūrvā for worship. After the offering, only one blade remained.
The guest told them that a little offered with devotion could satisfy him, while a great deal offered without devotion could fail.
They gave him the one remaining blade.
The text makes the turn immediate. The guest eats the blade and his hunger is extinguished. Then the disguise falls away and Gaṇeśa stands before them. He offers them a boon. They do not ask for wealth. They ask that their devotion remain firm and that they be freed from the difficult ocean of existence.
The revealed form has four arms and an elephant's trunk, with a lotus, an axe, a garland and a tusk in his hands. The starving guest is gone; the one they had been worshipping is standing in their house.
That story is later told to explain why dūrvā is offered to Gaṇeśa. But the Purāṇa does not stop with an explanation. It turns the lesson into a weighing test.
A sage tells his wife to take one blade of dūrvā and ask Indra for exactly its weight in gold — neither more nor less.
Indra sends her to Vaiśravaṇa, the keeper of divine wealth.
Vaiśravaṇa is astonished by the request. A blade of grass should be easy to match.
A goldsmith's scale is brought. The gold does not equal the blade. A merchant's scale is tried. Then another balance. Vaiśravaṇa adds one piece of gold, then many.
Still the side holding the dūrvā stays down.
He puts the entire treasury on the scale, piled up like a mountain. It is not enough. He summons his wife; she climbs onto the balance. Still not enough. Then he places his whole city there.
Indra hears what has happened and comes with his own wealth. He too cannot raise the blade. He thinks of Viṣṇu and Śiva; they come with their cities and join the test.
The blade does not rise.
The gods finally go to the sage and admit that they do not understand the power of the dūrvā he has offered to Gaṇeśa. The chapter ends by saying that even the three worlds are not equal in weight to one such blade.
A whole treasury, a city and the gods could not lift what one poor house had given with devotion.