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
Show Answer
Answer-D
Solution-
Solution(By Apex 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,
$\begin{array}{l}\Rightarrow72y+60\times6x=69(6x+y)\\
\Rightarrow72y+360x=414x+69y\\
\Rightarrow3y=54x\\
\Rightarrow y=18x\\
\text{Therefore,}\\
\text{Required average}\\
=\Large\frac{72 \times 18 x+60 \times 6 x+50 \times 7 x}{18 x+6 x+7 x} \\
=\Large\frac{1296+360+350}{31} \\
=\Large\frac{2006}{31} \\
=64.7
\end{array}$
