Question

The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200.
What is the monthly income of P?

Answer 1

(P+Q)/2=5050
=>P=10100-Q........................(i)
(Q+R)/2=6250
=>Q=12500-R.......................(ii)
(P+R)/2=5200
=>R=10400-P.......................(iii)
Now,
put value of Q from (ii) into (i)
P=10100-(12500-R)
P=R-2400.................................(iv)
again put value R from (iii) in to (iv)
P=(10400-P)-2400
P=4000
Ans :Monthly income of P is Rs. 4000

Answer 2

We can write three equations as follows:

P + Q / 2 = 5050; P + Q = 10100 (1)
Q + R / 2 = 6250 ; Q + R = 12500 (2)
P + R / 2 = 5200 ; P + R = 10400 (3)

Multiply equation (2) by -1 and add (1) + (2) P - R = - 2400 R = P + 2400
By replacing R in equation (3)
P + P + 2400 = 10400 , 2P = 8000
P = 4000