# 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

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### 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} \$\$