In 2011, the arithmetic mean of the annual incomes of Ramu
and Suresh was Rs. 3800. The arithmetic mean of the annual incomes of Suresh
and Trump was Rs. 4800, and the arithmetic mean of the annual incomes of Trump
and Ramu was Rs. 5800. What is the arithmetic mean of the incomes of the three?
a) 5200
a) 5200
b) 4800
c) 4400
d) 4000
e) None.
Answer: Option b
ReplyDeleteExplanation:
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, (a+b)/2=3800
Multiplying by 2 yields a+b=2×3800
a+b=7600.
The arithmetic mean of the annual incomes of Suresh and Pratap was Rs. 4800.
Hence, (b+c)/2=4800
Multiplying by 2 yields b+c=2×4800
b+c=9600.
The arithmetic mean of the annual incomes of Pratap and Ramesh was Rs. 5800.
Hence, (c+a)/2=5800
Multiplying by 2 yields c+a=2×5800
c+a=11,600
Summing 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:
=a+b+c)/3
=14,400/3
=4800