The average test score of a class of m students is 60 and that of n students is 81. When the scores of both classes are combined, then the average is 70. In this context, which of the following statements are correct?
A. (m + n)/(m − n) = 21
B. m/(m − n) = 11
C. n/(n + m) = 10
D. m/(m + n) = 11
E. n/(m − n) = 10
Choose the correct answer from the options given below:

Correct option is B

Given:
Average score of m students = 60
Average score of n students = 81
Combined average = 70
Formula:
Combined average = Total score / Total number of students
Solution:
Total score of m students = 60m
Total score of n students = 81n
Therefore,
(60m + 81n)/(m + n) = 70
60m + 81n = 70m + 70n
11n = 10m
Therefore,
m/n = 11/10
Let:
m = 11k
n = 10k
Now,
m − n = 11k − 10k
= k
Checking Statement A:
(m + n)/(m − n)
= (11k + 10k)/k
= 21
Therefore, A is correct.
Checking Statement B:
m/(m − n)
= 11k/k
= 11
Therefore, B is correct.
Checking Statement C:
n/(n + m)
= 10k/(10k + 11k)
= 10/21
Therefore, C is incorrect.
Checking Statement D:
m/(m + n)
= 11k/(11k + 10k)
= 11/21
Therefore, D is incorrect.
Checking Statement E:
n/(m − n)
= 10k/k
= 10
Therefore, E is correct.
Thus, the correct statements are A, B and E only.
Hence, the correct answer is Option (b) A, B, E only.