question_answer

The average age of the whole class is 12.05 years. The average age of all girls is 12.5 years and the average age of 45 boys is 11.75 years. What is the total number of girls in the class?

A)  27                               

B)  25

C) 40                   

D) 30                   

E)  None of these

Correct Answer: D

Solution :

Let the no. of girls be x. The no. of boys is 45.            Total age of boys and girls in the class \[=(x+45)\times 12.05\] Now, \[=(x+45)\times 12.05=45\times 11.75+x\times 12.5\] \[12.05x+542.25=528.75+12.5x\] or, 13.5 = 0.45x  \[\therefore \]x=30 Quicker   Method   (By Allegations Method): \[\Rightarrow \]If there, are 45 boys then no. of girls = 30