The average of the ages of A and B is 25 years, that of B and C is 30 years and that of C and A is 32 years. The age of C (in years) is:
- A39
- B37
- C35
- D32
Solution & Step-by-step Explanation
From the problem statements, we can form equations for the sums of their ages:
2
A+B
=25⟹A+B=50
2
B+C
=30⟹B+C=60
2
C+A
=32⟹C+A=64
Adding all three equations:
(A+B)+(B+C)+(C+A)=50+60+64
2(A+B+C)=174
A+B+C=87
To find the age of C, substitute A+B=50 into this equation:
50+C=87
C=87−50=37 years
2
A+B
=25⟹A+B=50
2
B+C
=30⟹B+C=60
2
C+A
=32⟹C+A=64
Adding all three equations:
(A+B)+(B+C)+(C+A)=50+60+64
2(A+B+C)=174
A+B+C=87
To find the age of C, substitute A+B=50 into this equation:
50+C=87
C=87−50=37 years