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There are 3 groups of students, each containing 25, 50 and 25 students respectively. The mean marks obtained by the first two groups are 60 and 55. The combined mean of all the three groups is 58. What is the mean of the marks scored by the third group ?
Answer & Solution
Correct Answer:
Option
E
Let the mean marks of the third group be x.
Then,
$$\eqalign{ & \Rightarrow \frac{{25 \times 60 + 50 \times 55 + 25 \times x}}{{25 + 50 + 25}} = 58 \cr & \Rightarrow 1500 + 2750 + 25x = 5800 \cr & \Rightarrow 25x = 1550 \cr & \Rightarrow x = 62 \cr} $$
Then,
$$\eqalign{ & \Rightarrow \frac{{25 \times 60 + 50 \times 55 + 25 \times x}}{{25 + 50 + 25}} = 58 \cr & \Rightarrow 1500 + 2750 + 25x = 5800 \cr & \Rightarrow 25x = 1550 \cr & \Rightarrow x = 62 \cr} $$
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