Three math classes: P,
Q and R, take an algebra test.
The average score in
class P is 83.
The average score in
class Q is 76.
The average score in
class R is 85.
The average score of all
students in classes P and Q together is 79.
The average score of all
students in classes Q and R together is 81.
What is the average for all the three classes?
a) 81.5
b) 81
c) 82.5
d) 82
e) None.
Answer: Option a
ReplyDeleteExplanation:
Average score of class P is 83 and that of class Q is 76 and the combined average of P and Q is 79.
By rule of alligation ratio of students in P:Q is given by
P : Q
79
/ \
83 76
3 : 4
Similarly, average score of class Q is 76 and that of class R is 85 and the combined average is 81.
By rule of alligation ratio of students in Q:R is
Q : R
81
/ \
76 85
4 : 5
P:Q:R=3:4:5
Total average for P, Q and R
=(3×83+4×76+5×85)/(3+4+5)
=81.5