# In 2011, the arithmetic mean of the annual incomes of Ramesh and Suresh was Rs. 3800. The arithmetic mean of the annual incomes of Suresh and Pratap was Rs. 4800, and the arithmetic mean of the annual incomes of Pratap and Ramesh was Rs. 5800. What is the arithmetic mean of the incomes of the three?

A. Rs. 4000

B. Rs. 4200

C. Rs. 4400

D. Rs. 4800

Let a, b, and c be the annual incomes of Ramesh, Suresh, and Pratap, respectively. Now, we are given that The arithmetic mean of the annual incomes of Ramesh and Suresh was Rs. 3800. Hence, $\begin{array}{l}\Large\frac{a+b}{2}=\small3800\\ \Rightarrow a+b=2\times3800=7600\end{array}$ The arithmetic mean of the annual incomes of Suresh and Pratap was Rs. 4800. Hence, $\begin{array}{l}\Large\frac{b+c}{2}=\small4800\\ \Rightarrow b+c=2\times4800=9600\end{array}$ The arithmetic mean of the annual incomes of Pratap and Ramesh was Rs. 5800. Hence, $\begin{array}{l}\Large\frac{c+a}{2}=\small5800\\ \Rightarrow c+a=2\times5800=11,600\end{array}$ 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, $\begin{array}{c}\Large\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{3}\\ =\Large\frac{14,400}{3}\\ =\mathrm{Rs}.4800\end{array}$