Lets say Mrs Ang had X amount of money:

1) After spending 1/6X on a ring she will have 5/6X remaining;

2) After spending half of the remaining (5/6X) on a necklace she will have 5/12X remaining;

3) After receiving $1330 from her daughter, her money increased to twice her original amount, which is 2X;

4) Hence 2X = 5/12X + 1330
Subtracting 5/12X from both sides, 19/12X = 1330, hence X (Mrs Angs original amount of money) = 840.

Since she spent Half of her remaining (5/6X) on the necklace, she would have spent 5/12X, hence 5/12 x 840 = 350

Hence she spent $350 on the necklace