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The average weight of 10 boys is 45 kg. If the weight of the teacher is added, the average weight increases by 2 kg. What is the weight of the teacher?
65 kg
67 kg
69 kg
71 kg
67 kg
The correct answer is 67 kg. The total weight of 10 boys is 450 kg, calculated by multiplying 10 by 45. When the teacher is included, the total number of persons becomes 11 and the average increases by 2 kg to become 47 kg, resulting in a new total weight of 517 kg. Subtracting the initial total weight of the boys from this new total gives the teacher's weight of 67 kg.
The correct answer is 67 kg. The total weight of 10 boys is 450 kg, calculated by multiplying 10 by 45. When the teacher is included, the total number of persons becomes 11 and the average increases by 2 kg to become 47 kg, resulting in a new total weight of 517 kg. Subtracting the initial total weight of the boys from this new total gives the teacher's weight of 67 kg.
Averages form a fundamental quantitative concept tested regularly in recruitment examinations conducted by the Railway Recruitment Board (RRB) to assess numerical efficiency.
Total weight of a group is calculated as the product of the number of entities and their average.
When a new member joins and the average increases, the new total weight includes the increment distributed across all members.
Shortcut method: New average plus the product of the increment and the new total count yields the new entry value.
Quick calculation shortcut: 45 + (11 times 2) equals 67 kg.
Option A (65 kg) is incorrect due to a subtraction or sign error during calculation.
Option C (69 kg) and Option D (71 kg) result from incorrect scaling factors applied to the average increment.
B is correct тАФ The weight of the teacher is 67 kg as derived from the difference in total group weights.
Mastering shortcut formulas for averages helps drastically reduce solving time in speed-based computer-based tests like RRB JE CBT-1.
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