Three maths classes: X, Y, and Z take an algebra test. The average score of class X is 83. The average score of class Y is 76. The average score of class Z is 85. The average score of class X and Y is 79 and the average score of class Y and Z is 81. What is the average score of the combined classes X, Y, and Z? - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
79.5
B
81.5
C
83.5
D
85.5

Solution:

The average score of class X = 83
The average score of class Y = 76
The average score of class Z = 85
The average score of class X and Y = 79
The average score of class Y and Z = 81
Let us assume that the number of students in class X, Y, and Z are a, b, and c respectively, and the sum of the scores of the students in class X, Y, and Z are p, q, and r.

\frac{p}{a}

= 83,

\frac{q}{b}

= 76,

\frac{r}{c}

= 85

\frac{p + q}{a + b} = 79

and

\frac{q + r}{b + c} = 81

\Rightarrow p + q = 79 a + 79 b

\Rightarrow 83 a + 76 b = 79 a + 79 b

\Rightarrow 4 a = 3 b

\Rightarrow b = \frac{4 a}{3}

And

q + r = 81 b + 81 c

\Rightarrow 76 b + 85 c = 81 b + 81 c

\Rightarrow 4 c = 5 b

\Rightarrow c = \frac{5 b}{4} = \frac{5}{4} \times \frac{4 a}{3} = \frac{5 a}{3}

Average score of the combined class X, Y, and Z =

\frac{p + q + r}{a + b + c} = \frac{83 a + 76 b + 85 c}{a + b + c} = 81.5

Solution:

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