The average age of A and B is 20 years. If C were to replace A, the average age would be 19, and if C were to replace B, the average age would be 21. What are the ages of B and C?
Answers
Step-by-step explanation:
A+B/2=20 A+B=40
B+C/2=19 B+C=38
C+A/2=21 C+A=42
BY SUBTRACTING A+B=40 AND B+C=38 WE GET A+B-B-C=40-38 A-C=2
BY ADDING A+C=42 AND A-C=2 WE GET 2A=44 A=22
A+C=42 C=42-22=20 C=20
A+B=40 B=40-22 B=18
A=22,B=18,C=20
option B
A+B=2*20;
C+B=2*19;
A+C=2*21;
By solving the above equations we get the solution
A+B/2=20 A+B=40---------1
C+B/2=19 C+B=38----------2
C+A/2=21 C+A=42----------3
BY SUBSTRACTING 1&2 A+B=40 AND B+C=38 WE GET A+B-B-C=40-38
A-C=2
NOW SOLVING A-C=2 & A+C=42
2A=44
A=22
SUBSTITUTE A=22 IN A-C=2
C=22-2
C=20
SUBSTITUTE C=20 IN B+C=38
B=38-C
B=38-20
B=18
Answer:
Average age of A and B = 20 years
A+B/2 = 20
A+B=40
Average age of C and B = 19 years
C+B/2 = 19
C+B=38
Average age of A and C =21 years
A+C/2 = 21
A+C=42
A+C-A-B=2
C-B=2
B+C+B-C=38-2
2B=36
B=18
C=20
A=12