What is the average age of 46 students studying in a class? I. The average age of boys is 15.4 yr while the average age of girls is 14.6 yr. II. Boys and girls are respectively in the ratio 4: 5. III. The number of boys is less than that a girls by 5.
A) I and either II or III
B) I and II
C) I and III
D) All I, II and III
E) None of the above
Correct Answer: A
$ \therefore $ Number of boys $ =\frac{4}{9}\times 45=20 $ Number of girls $ =25 $ I. Average age $ =\frac{15.4\times 20+14.6\times 25}{45} $ $ =\frac{308+365}{45}=14.95yr $ III. Let the number of girls be $ x. $
$ \therefore $ Number of boys $ =x-5 $
$ \therefore $ $ x+x-5=45 $
$ \Rightarrow $ $ 2x=50 $
$ x=25 $
Hence, statement I and either II or III will give the solution.