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The average weight of 12 bags of rice is 45 kg. When the weights of 3 bags of rice weighing \((w+5)\) kg, \((w-15)\) kg, and \((w+40)\) kg are added, the average weight increases by 2 kg. Find the value of \(w\).

1. 30 kg
2. 35 kg
3. 40 kg
4. 45 kg

Correct answer: 45 kg

Solution

The total weight of 12 bags is 12 × 45 = 540 kg. After adding 3 bags, the average becomes 47 kg for 15 bags, so total weight becomes 15 × 47 = 705 kg. Thus, the three added bags weigh 165 kg, giving (w+5) + (w−15) + (w+40) = 165, so 3w + 30 = 165 and w = 45.

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