Question
Download Solution PDFThe average weight of 12 bags of rice is 45 kg. When the weights of 3 bags of rice with weights (w+5) kg, (w−15) kg, and (w+40) kg are added, the average weight is increased by 2 kg. Find the value of 'w'.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven data:
Average weight of 12 bags = 45 kg
⇒ Total weight = 12 × 45 = 540 kg
3 more bags are added:
Weights are: (w + 5), (w − 15), and (w + 40)
⇒ Total of new bags = (w + 5) + (w − 15) + (w + 40) = 3w + 30
New total number of bags = 12 + 3 = 15
New average = 45 + 2 = 47 kg
⇒ New total weight = 15 × 47 = 705 kg
Total new weight = Old weight + 3 new bags
⇒ 540 + (3w + 30) = 705
⇒ 3w + 30 = 705 − 540 = 165
⇒ 3w = 165 − 30 = 135
⇒ w = 135 ÷ 3 = 45
Thus, the correct answer is 45 kg.
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