A and B have their annual average income Rs. 80,000.B and C have their annual average income Rs. 75,000. C and A have their annual average income Rs. 78,000.The annual income of A is ?

Let the annual incomes of A, B and C be $$a$$, $$b$$ and $$c$$ respectively.

Average income of A and B is given as Rs. 80,000.
Hence,

$$\frac{a+b}{2}=80000 \;\Longrightarrow\; a+b = 2 \times 80000 = 160000$$ $$-(1)$$

Average income of B and C is given as Rs. 75,000.
Therefore,

$$\frac{b+c}{2}=75000 \;\Longrightarrow\; b+c = 2 \times 75000 = 150000$$ $$-(2)$$

Average income of C and A is given as Rs. 78,000.
So,

$$\frac{c+a}{2}=78000 \;\Longrightarrow\; c+a = 2 \times 78000 = 156000$$ $$-(3)$$

Add equations $$(1), (2)$$ and $$(3):$$

$$(a+b) + (b+c) + (c+a) = 160000 + 150000 + 156000$$

$$2(a+b+c) = 466000$$

$$a + b + c = \frac{466000}{2} = 233000$$ $$-(4)$$

To find $$a$$ (income of A), subtract $$(2)$$ from $$(4):$$

$$a = (a+b+c) - (b+c) = 233000 - 150000 = 83000$$

Therefore, A’s annual income is Rs. 83,000.

Option C which is: Rs. 83000