a) Rs. 4000
b) Rs. 4200
c) Rs. 4400
d) Rs. 4800
Answer: d
Explanation: Let a, b, and c be the annual incomes of Ramesh, Suresh, and Pratap, respectively.
The arithmetic mean of the annual incomes of Ramesh and Suresh was Rs. 3800.
$$\frac{{{\text{a}} + {\text{b}}}}{2}$$ = 3800
a + b = 2 × 3800 = 7600
The arithmetic mean of the annual incomes of Suresh and Pratap was Rs. 4800.
$$\frac{{{\text{b}} + {\text{c}}}}{2}$$ = 4800
b + c = 2 × 4800 = 9600
The arithmetic mean of the annual incomes of Pratap and Ramesh was Rs. 5800.
$$\frac{{{\text{c}} + {\text{a}}}}{2}$$ = 5800
c + a = 2 × 5800 = 11,600
Adding these three equations yields:
(a + b) + (b + c) + (c + a) = 7600 + 9600 + 11,600
2a + 2b + 2c = 28,800
a + b + c = 14,400
The average of the incomes of the three equals the sum of the incomes divided by 3,
$$\eqalign{
& \frac{{{\text{a}} + {\text{b}} + {\text{c}}}}{3} \cr
& = \frac{{14,400}}{3} \cr
& = {\text{Rs}}{\text{.}}\,4800 \cr} $$
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