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An old woman had the following assets:

  1. Rs. $70$ lakh in bank deposits
  2. $1$ house worth Rs. $50$ lakh
  3. $3$ flats, each worth Rs. $30$ lakh
  4. Certain number of gold coins, each worth Rs. $1$ lakh

She wanted to distribute her assets among her three children; Neeta, Seeta and Geeta. The house, any of the flats or any of the coins were not to be split. That is, the house went entirely to one child; a flat went to one child and similarly, a gold coin went to one child.

The value of the assets distributed among Neeta, Seeta and Geeta was in the ratio of $1:2:3$, while the gold coins were distributed among them in the ratio of $2:3:4$. One child got all three flats and she did not get the house. One child, other than Geeta, got Rs. $30$ lakh in bank deposits.

How many gold coins did the old woman have?

  1. $72$
  2. $90$
  3. $180$
  4. $16$
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