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The average age of 15 students in a class is 14 years. If the teacher's age is included, the average increases by 2 years. What is the age of the teacher?
42 years
44 years
46 years
48 years
46 years
Shortcut: Old Average + (New Total Count × Increase in Average) = 14+16×2=46 years.
Number of students = 15, Average age of students = 14 years, Increase in average = 2 years
Teacher’s Age=(n+1)×Anew−n×Aold
Shortcut: Old Average + (New Total Count × Increase in Average) = 14+16×2=46 years.
Multiplying the increase in average by the original number of students (15) instead of the new total number of persons (16).
Calculate Initial Total Age
Find the sum of ages of the 15 students by multiplying the number of students by their average age.
Total Age=15×14=210
Calculate New Total Age
With the teacher included, the total number of people becomes 16, and the new average is 14+2=16 years.
New Total Age=16×16=256
Find Teacher's Age
Subtract the initial total age of the students from the new total age to find the teacher's age.
Teacher’s Age=256−210=46
C is correct because the teacher's age is calculated as 46 years.
Mastering weighted averages and balancing sums will save crucial time in RRB CBT-1 data interpretation and arithmetic sections.
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