Aptitude - Average - Discussion

p+q=5050*2=10100
q+r=6250*2=12500
p+r=5200*2=10400
than the total income is (p+q)+(q+r)+(p+r)= 133000
we have 2(p+q+r)=133000
next 2 dividing to 133000

It become p+q+r=16500
then we apply q+r values in there place
p+12500=16500
p=16500-12500
p=4000

Ok?

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 why did we subtract from (ii) ?

2p=2(5050+5200-6250)
=>p=4000

Simple method:.

p+q+r = 5050+5200 = 10250.

We have to subtract q+r from it. (ie) 6250.

10250-6250 = 4000 answer.

It's not p=4000 it's p=2000
Let me explain
p+q=5050
q+r=6250
p+r=5200
Therefore we can write -
2(p+q+r)= 16500
p+q+r=16500/2
= 8250
p=8250-(q+r)
But we know that
q+r=6250
p=8250-6250
=2000
Hence p=2000
I hope everyone understand it.

Friends p=4000 and not 2000.please read the question properly!!they have asked WHAT IS THE MONTHLY INCOME OF P AND NOT WHAT IS THE AVERAGE INCOME OF P.it is given "the average (THE KEY WORD IS AVERAGE!!) monthly income of P and Q is 5050" which means [(p+q)/2] = 5050.therefore the monthly income of p+q = 10100.
similarly the average income of q+r is 6250 which means [(q+r)/2]=6250.therefore the monthly income of q+r = 12500
and in the same manner,the average income of p+r is 5200 which means [(p+r)/2]=5200.therefore the monthly income of p+r is 10400.Now add p+q=10100 and p+r = 10400.therefore the answer is p+q+p+r=10100+10400=20500.So we get 2p+q+r=20500.now minus this with THE MONTHLY INCOME q+r=12500.The result is [(2p+q+r)-(q+r)]=[(20500)-(12500)]=8000.
so 2p=8000 (SINCE Q AND R GET CANCELLED)
P=4000

@Praveen's process simple n right..but he forget multiply r.h.s with 2 because it is average of two items.

P + Q = (5050 x 2) = 10100
Q + R = (6250 x 2) = 12500
P + R = (5200 x 2) = 10400

add above three

2(p+q+r)=33000
(p+q+r)=16500

we need 'p' only so

(p+q+r)-(q+r)=16500-12500

so p=4000...

p+q= 5050
p+r=5200
total= 10250
here substract(-)q+r = 6250
p = 4000 (ans)

(p+q)/2 = 5050...(1)
(q+r)/2 = 6250...(2)
(p+r)/2 = 5200...(3)

From (1) and (2)

q=10100-p
r = 12500-q
Sub in (3)

p=10400-r
=10400-12500+q
=10400-12500+10100-p
p=(10400-12500+10100)/2=4000.