Aptitude - Average - Discussion

It can also done as (i) + (iii) - (ii).

Dude can we do like this ?
p+q=5050
q+r=6250
p+r=5200
p+q+q+r+p+r=16500
2(p+q+r)=16500
p+q+r=8250
hence p+q+r-(q+r)=p+q+r-q-r=>
p=8250-6250=4000

Any one can explain briefly ? i dont understand the last step..

Lets p's income=x,q's income=y and r's income=z
now p and q earn 5050 (avg income of p and q)
i;e (x+y)/2=5050.......(1)
similarly q and r earn 6250 (avg income of q and r)
i;e (y+z)/2=6250........(2)
again p and r earn 5200 (avg income of p and r)
i;e (x+z)/2=5200........(3)
now by using equations 1,2,3you have to find out the value of x
so now add equation 1 and 3
(x+y+x+z)/2=5050+5200
=>(2x+y+z)/2 = 10250.....(4)
now subtract equation 2 from this
=>(2x+y+z-y-z)/2=10250-6250
=>2x/2=4000
=>x=4000
thats p's income

Excellent praveen.

8250-6250=2000
but how did we get 4000

We can also do like this..
p+q=5050
therefore p=5050-q --->(1)
q+r=6250
therefore r=6250-q --->(2)
p+r=5200 --->(3)
substitute (1) and (2) in (3)
thus we get
5050-q+6250-q=5200
q=3050 --->(4)
substitute (4) in (1)
thus p=5050-3050
p=2000
when p working with q, p's income is 2000
substitute (4) in (2)
r=6250-3050
r=3200--->(5)
substitute (5) in (3)
we get p=2000
when p working with r, p's income is 2000
therefore total income working with q and r is 2000+2000=4000
thus 4000 is the income of p

Why we are multiplying every equation with 2 only in RHS?

You are absolutely right Praveen.

@Praveen can you help me

Hence p+q+r-(q+r)=p+q+r-q-r=>

p=8250-6250=4000