This question arose when I tried solving one of the math problems below,
Question: The average monthly income of Rakesh and Suresh is Rs. 5050. The average monthly income of Suresh and Ramesh is Rs. 6250 and the average monthly income of Rakesh and Ramesh is Rs. 5200. What is the monthly income of Rakesh?
Answer: Rakesh +Suresh (total income) = 5050 x 2 = 10100.... (i) Suresh +Ramesh (total income) = 6250 x 2 = 12500.... (ii) Rakesh+ Ramesh (total income) = 5200 x 2 = 10400.... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500.... (iv) Subtracting (ii) from (iv), we get P = 4000. So, Rakesh's monthly income = Rs. 4000
When I tried solving the above problem with this method shown below, it gives different Answer Why?
My Answer: Let Rakesh = x, Suresh = y , Ramesh = z. Then the above statements can be written as,
x+y = 5050 --1st equation
y+z = 6250 --2nd equation
z+x = 5200 --3rd equation
Solving the 1st and 2nd equations we get x-z = -1200 Which can be written x= z-1200 Which is substituted in the 3rd equation, So that z + (z-1200) = 5200 ==> 2z = 6400 ==> z = 3200 Now substitute z = 3200 in 3rd equation, we get x = 2000 which is Rakesh's Monthly Income.
Why I get the wrong answer 2000 instead of the right answer 4000 which follows a different method?.
The system of equations should be the following: $$x+y=10100$$ $$y+z=12500$$ $$z+x=10400$$ You forgot to multiply the incomes by $2$ because they're the averages.