Question

2.
In a class the average age of boys is 14 years and the average age of girls is
12 years. If there are 44 students in the class and average age of the class is
13.5 years, then find the ratio of number of girls to the number of students
in the class.
(A) 1:3
(B) 2:3 (C) 1:4 (D) 3:2
(E) None of these​

Answer 1

(C)1:4

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Step-by-step explanation:

Let the no. of boys be x

Then the no. of girls=44-x

Average age of boys=14 years

Sum of ages of all boys=14 × x =14x

Average age of girls = 12 years

Sum of ages of all girls=12(44-x) =528-12x

Average =total sum of ages of all students ÷ total no. of students

=(14x + 528 - 12x) ÷ 44

But, average age of class=13.5(given)

A/Q => (14x + 528 - 12x)/44 = 13.5

=> 2x + 528 = 13.5 × 44

=> 2x = 594-528=66

=>x=66/2

=>x=33

Hence,total no. of boys=33

Total no. of girls=44-33=11

Ratio=11/44=1:4

So the answer is (C)