First slide

Introduction to statistics

Question

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys, in the class is

Easy

A

40%
B

20%
C

80%
D

60%

Solution

Let the number of boys and girls be r and y.
$\begin{array}{lc} ∴ & 52 x + 42 y = 50 (x + y) \\ \Rightarrow & 52 x + 42 y = 50 x + 50 y \\ \Rightarrow & 2 x = 8 y \Rightarrow x = 4 y \end{array}$
$∴$ Total number of students in the class $= x + y = 4 y + y = 5 y$
$∴$ Required percentage of boys $= (\frac{4 y}{5 y} \times 100) % = 80 %$

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