Question
The average weight of 20 boys is
48 kg. However, the weights of three boys, originally 46 kg, 44 kg, and 38 kg, were incorrectly recorded as 'k' kg, 'k+2' kg, and 'k−4' kg, respectively. When the correct weights are used, the average weight increases by 0.5 kg. Determine the value of 'k'.Solution
ATQ, (48 × 20 – k – (k + 2) – (k – 4) + 46 + 44 + 38)/20 = 48 + 0.5 (960 – k – k – 2 – k + 4 + 128)/20 = 48.5 1088 – 3k + 2 = 970 1090 – 3k = 970 3k = 1090 – 970 3k = 120 k = 40
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