Mr. T has a wrong weighing pan. One arm is lengthier than the other. 1…

Concept: A weighing balance with unequal arm lengths adds a fixed, hidden bias to whichever pan sits on the longer arm — the longer arm exaggerates the true torque on its side. When the SAME 1 kg weight is balanced twice, once resting on the longer arm and once on the shorter arm, that bias enters the two balance equations with opposite sign. Adding the two equations cancels the bias and leaves a direct relationship for the unknown item weight.

Application:

1. Let m = weight of one melon (in kg) and x = the constant bias the longer arm contributes to whichever pan it carries.

2. 1 kg on the left balances 8 melons on the right: 1 + x = 8m.

3. 1 kg on the right balances 2 melons on the left (the bias now works the opposite way): 1 − x = 2m.

4. Add the two equations to eliminate x: (1 + x) + (1 − x) = 8m + 2m, i.e. 2 = 10m.

5. Solve for m: m = 2/10 = 0.2 kg = 200 gm.

Cross-check: Subtracting the two equations gives 2x = 6m, so x = 3m = 0.6 kg. Substituting back: 1 + 0.6 = 1.6 = 8 × 0.2 (first condition holds), and 1 − 0.6 = 0.4 = 2 × 0.2 (second condition holds too) — both stated balance readings are satisfied together only at m = 200 gm.

So the weight of a single melon is 200 gm.