The average monthly income of A and B is ₹5,050, the average monthly income of B and C is ₹6,250, and the average monthly income of A and C is ₹5,200. What is the sum of the monthly incomes (in ₹) of A, B and C?
- A18000
- B16500
- C19500
- D11000
Solution & Step-by-step Explanation
From the problem statements, we can set up equations for the sums of their incomes:
2
A+B
=5050⟹A+B=10100
2
B+C
=6250⟹B+C=12500
2
A+C
=5200⟹A+C=10400
Adding all three equations together:
(A+B)+(B+C)+(A+C)=10100+12500+10400
2(A+B+C)=33000
Dividing by 2 to find the sum of their monthly incomes:
A+B+C=
2
33000
=16500
2
A+B
=5050⟹A+B=10100
2
B+C
=6250⟹B+C=12500
2
A+C
=5200⟹A+C=10400
Adding all three equations together:
(A+B)+(B+C)+(A+C)=10100+12500+10400
2(A+B+C)=33000
Dividing by 2 to find the sum of their monthly incomes:
A+B+C=
2
33000
=16500