A coaching institute has students in 3 batches X Y and…

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A coaching institute has students in 3 batches – X, Y and Z. In a certain examination, the average marks obtained by these batches are 72, 60 and 50 respectively. The average marks of batches X and Y taken together is 69. If the ratio of the number of students in batches Y and Z is 6 : 7. What is the average score of all the three batches put together?

  1. A. 59
  2. B. 61.6
  3. C. 63.5
  4. D. 64.7

E. 65

Here is complete explanation of A coaching institute has students in 3 batches X Y and….

Solution(By ExamCraze Team)

Let the number of students in batches Y and Z be 6x and 7x respectively, and the number of students in batch X be y.
Then,
$$eqalign{ & Rightarrow 72y + 60 times 6x = 69left( {6x + y} right) cr & Rightarrow 72y + 360x = 414x + 69y cr & Rightarrow 3y = 54x cr & Rightarrow y = 18x cr} $$
∴ Required average

$$eqalign{ & = frac{{72 times 18x + 60 times 6x + 50 times 7x}}{{18x + 6x + 7x}} cr & = frac{{1296 + 360 + 350}}{{31}} cr & = frac{{2006}}{{31}} cr & = 64.7 cr} $$

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