Question : The average age of eight girls is y years. 5 new girls having ages (in years) given by y + 3, y – 6, y + 15, y + 8, and y + 6 join the class. What is the new average age of the class?
Option 1: (y + 2) years
Option 2: (y + 6) years
Option 3: (y + 3) years
Option 4: (y + 1) years
Correct Answer: (y + 2) years
Solution :
The average age of eight girls = y years
Ages of 5 new girls = y + 3, y – 6, y + 15, y + 8, y + 6
New average = $\frac{\text{Sum of all ages}}{\text{Total number of girls}}$
The sum of the ages of the eight girls = 8y
The sum of the ages of the new girls = (5y + 26)
Therefore, the sum of the ages of all 13 girls after the new girls join = 8y + 5y + 26 = 13y + 26
The total number of girls in the class is = 8 + 5 = 13
Using the formula,
New average = $\frac{\text{Sum of all ages}}{\text{Total number of girls}}=\frac{13\text{y} + 26}{13}= \text{y}+ 2$
Hence, the correct answer is y + 2 years.
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