One cone balances with 9 marbles. Since it is given that three cubes and one cone balance on a scale with 12 marbles and one cone balances with one cube and eight marbles.
It is given that,
3 cubes + 1 cone = 12 marbles and
1 cone = 1 cube + 8 marbles
Then,
3 cubes + 1 cube + 8 marbles = 12 marbles
⇒ 4 cubes = 12 marbles - 8 marbles
⇒ 4 cubes = 4 marbles
∴ 1 cube = 1 marble
Thus,
from the given,
1 cone = 1 cube + 8 marbles
⇒ 1 cone = 1 marble + 8 marbles
∴ 1 cone = 9 marbles
Therefore, one cone balances 9 marbles.
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