Examveda

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?

A. 59

B. 61.6

C. 63.5

D. 64.7

E. 65

Solution(By Examveda 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 = 69\left( {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}

This Question Belongs to Arithmetic Ability >> Average

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