Ok! the arm that is lengthier is heavier. from the question it is evident that the left arm is heavier.

Let the weight of the heavier arm w/o anything placed in its pan be i kg and that of the other arm be j kg. Let x kg be the weight of a melon

case 1:

1 kg on left balances 8 melons on right

so i + 1 j + 8x or i -j 8x - 1

case 2:

2 melons on left balances 1 kg on right

so i + 2x j + 1 or i - j 1 - 2x

from the 2 equations we get

8x - 1 1 - 2x

or x 1/5 kg

Answer is :

Weight of Melon 250 g

441 grams