Aptitude - Average - Discussion

7. 

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. The monthly income of P is:

[A]. 3500
[B]. 4000
[C]. 4050
[D]. 5000

Answer: Option B

Explanation:

Let P, Q and R represent their respective monthly incomes. Then, we have:

P + Q = (5050 x 2) = 10100 .... (i)

Q + R = (6250 x 2) = 12500 .... (ii)

P + R = (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.

P's monthly income = Rs. 4000.


Ratnakar said: (Aug 27, 2010)  
It can also done as (i) + (iii) - (ii).

Praveen said: (Nov 30, 2010)  
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

Sudhagar said: (Dec 11, 2010)  
Any one can explain briefly ? i dont understand the last step..

Tarun said: (Dec 13, 2010)  
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

Loverboy said: (Dec 19, 2010)  
Excellent praveen.

Soumya said: (Jan 8, 2011)  
8250-6250=2000
but how did we get 4000

Deepa said: (Jan 14, 2011)  
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

Shree Hema said: (Feb 13, 2011)  
Why we are multiplying every equation with 2 only in RHS?

Sonu said: (Feb 28, 2011)  
You are absolutely right Praveen.

Isha said: (Aug 20, 2011)  
@Praveen can you help me

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

p=8250-6250=4000

Thimoty said: (Aug 22, 2011)  
Praveen you are answer is good.

Prabhjeet said: (Sep 15, 2011)  
p+q=10100..........eq 1
q+r=12500.........eq 2
p+r=10400...........eq 3

subtracting 2 from 1 we get,

p+q-q-r=10100-12500
p-r=-2400.......eq 4
adding eq3 to eq 4

p-r+r+p=10100+(-2400)

2p=8000
p=4000

Rite ans.

Yazhini said: (Sep 19, 2011)  
No confusion we can do like this

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

We need only p so

p+q-(q+r)+p+r = p+q-q-r+p+r= 2P(cancel r and q)

10100-12500+10400=8000

2P = 8000

P = 4000.

Sundarsac said: (Sep 19, 2011)  
P + Q = (5050 x 2) = 10100 .... (i)

Q + R = (6250 x 2) = 12500 .... (ii)

P + R = (5200 x 2) = 10400 .... (iii)

the above three equation need not multiplied by 2 we can get without multiplying by 2(because its only short metod)

Swathi said: (Sep 28, 2011)  
4 A secret can be told only 2 persons in 5 minutes. The same person tells to 2 more persons and so on. How long will take to tell it to 768 persons?

A) 47. 5 min b) 50 min c) 500 min d) 49 min.

Can anyone help me in finding the solution for this problem as soon as possible ?

Yesu Babu Pagidimalla said: (Oct 7, 2011)  
Income of p=5050+5200-6250
=10250-6250
=4000

Amandha said: (Oct 16, 2011)  
Praveen is wrong why means 8250-6250=2000 not 4000.

Sunil said: (Oct 19, 2011)  
Please help me for this 8250-6250= 4000.

Sai Kumar said: (Nov 21, 2011)  
Simple method:

p+q+r=5050+5200=10250
we have to subtract q+r from it.. (ie)6250
10250-6250=4000 ans

Samar said: (Nov 26, 2011)  
p+q=5050
q+r=6250
p+r=5200
p+q+q+r+p+r=5050+6250+5200
2(p+q+r)=16500
p+q+r=16500/2
=8250
p+6250+8250
p=8250-6250
p=2000(Ans

A get the 2000Ans
How it comes 4000?

Please help me.

Mani.Bandavath said: (Dec 18, 2011)  
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?

Sana. said: (Feb 6, 2012)  
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) ?

Siva said: (Mar 22, 2012)  
2p=2(5050+5200-6250)
=>p=4000

Md Hasim And Km Roy said: (Mar 30, 2012)  
Simple method:.

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

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

10250-6250 = 4000 answer.

Sunil said: (Apr 27, 2012)  
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.

Upcoming Aptitude Warrior said: (Aug 17, 2012)  
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

Clarification said: (Aug 27, 2012)  
@Praveen's process simple n right..but he forget multiply r.h.s with 2 because it is average of two items.

Shiva said: (Aug 27, 2012)  
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...

Srinivas said: (Sep 27, 2012)  
p+q= 5050
p+r=5200
total= 10250
here substract(-)q+r = 6250
p = 4000 (ans)

Rahul said: (Nov 9, 2012)  
(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.

Srikanth said: (Aug 26, 2013)  
Why we do like:

5050*2 =

6250*2=

From where we get this 2 value.

Can you explain any one?

Miital said: (Aug 30, 2013)  
p and Q = 5050.

Q and R = 6250.

P and R = 5200.

NOW TOTAL OF

P AND Q = 5050.

P AND R = 5200.

= 10250.

NOW(10250-6250) = 4000.

Mahesh said: (Oct 3, 2013)  
p+q = 10100
p+r = 10400
q+r = 12500

q+r = 12500
p+r = 10400(-)
---------------
q-p = 2100

p+q = 10100
-p+q = 2100 (-)
-------------
2p = 8000

p = 4000.

Vishesh said: (Nov 13, 2013)  
@Praveen how did you get -(q+r) can you explain in detail?

Avinash Kumar Maurya said: (Dec 10, 2013)  
p/2+q/2 = 5050-------1.
q/2+r/2 = 6250--------2.

from equation 2,
q/2 = 6250-r/2.

Put equation 1 in q/2.

p/2+6250-r/2 = 5050.
p/2-r/2 = 5050-6250.
p/2-r/2 = -1200.

According 3 condition,

p/2+r/2 = 5200-------3.

From add 2 and 3,

p/2-r/2+p/2+r/2 = -1200+500.

p/2+p/2 = 4000.
p = 4000.

Shazeab Choudhary said: (Dec 11, 2013)  
6250-5050 = 1200.
5200-1200 = 4000.

Bhiksham Marepally said: (Jan 31, 2014)  
Hi @Swathi, the answer for your question is 47.5 minutes.

How means,
For 5 minutes secret can be told to 2 people,
In the next 5 minutes 2 people can told to another 2 people each so total 4 in second 5 minutes.
3rd 5 minutes 8.
4th 5 minutes 16.
.........
.........
9th 5 minutes 512.

Now the completed minutes are 9*5=45 minutes and secret reached to 512 persons.

In the next 5 minutes it can reach to 1024 people but we don't have 1024 people, we have only 768 people..so the people who didn't get the secret till now are 256.

So within 2.5 minutes if the persons in (512/2) told secret to one person each, then the secret will be reaching to 768 people in 45+2.5 = 47.5 minutes.

Ananthi Ck said: (Mar 4, 2014)  
P and Q = 5050.
Q and R = 6250.
P and R = 5200.

We need income of p.

So 6250-5050 = 1200.

5200 - 1200.

= 4000.

Ananthi Ck said: (Mar 9, 2014)  
Let p&q =5050---(1).
q& r = 6250 --- (2).
p&r = 5200---(3).

We have to find p?
So, (1)+(3)p&q+p&r = 5050+5200.

p&Q&r = 10250 already given q&r = 6250.

We need to find p only, so p = (p&Q&r)10250 -(q&r)6250 (1)+(3)-(2).

p = 4000.

Aaditya said: (Aug 31, 2014)  
If the average income of 10 persons is Rs. 21 and the average income of 150 persons is Rs. 25. Then find the average income of 50 persons.

Teja said: (Sep 8, 2014)  
P and Q is Rs. 5050.
P and R is Rs. 5200.
Q and R is Rs. 6250.

5050+5200-6250 = 4000.

Mayur said: (Oct 6, 2014)  
5050+5200+6250 = 16500 Now Q and R is 6250 i.e 2*6250 = 12500.

Now P is 16500-12500 = 4000.

Tin said: (Oct 14, 2014)  
Why we need to subtract 6250? I can hardly understand.

Akash said: (Dec 18, 2014)  
P&Q = 5200.
Q&R = 6250.
P+R = 5200.

= ((P+Q) + (P+R)) - (Q+R).

== (5050+5200) - 6250.

= 4000.

Reejesh said: (Jan 4, 2015)  
Hi All,

Can this be done in this way?

Average of

(i) PQ = 5050.
(ii) QR = 6250.
(iii) PR = 5200.

Total 10250.
10250-6250 = 4000.

B.E(Bekar Engg) said: (Mar 4, 2015)  
(p+q) + (q+r) + (p+r) here p, q, r comes two time;

So that, 2(p+q+r) =16500.

16500/2 = 8250;

p+q+r = 8250;

q+r = 6250;

8250-6250 = 2000;

As above mention p is 2 time. So 2(2000) = 4000;

Kiran said: (Mar 17, 2015)  
P & Q = 5050.
Q & R = 6250.
P & R = 5200.

= 5050/2 + 6250/2 + 5200/2.
= 2525+3125+2600.
= 8250-6250.
= 4000/-.

Aarthi said: (May 13, 2015)  
p+q = 5050.
q+r = 6250.
p+r = 5200.

We have to add this three equations P+q+q+r+p+r = 16500.

Then we get 2(p+q+r) = 16500.

p+q+r = 8250.
q+r = 6250.

We want to solve the above two equations then we get p = 2000.

For me the correct value is 2000.

Vinay said: (Jul 30, 2015)  
P+Q = 5050*2 = 10100.
Q+R = 6250*2 = 12500.
P+R = 5200*2 = 10400.

P+Q + Q+R + P+R = 33000.

2P+2Q+2R = 33000.
2(P+Q=R) = 33000.

So, P+Q+R = 16500.

P+12500 = 16500. Because Q+R = 12500.

Hence P = 16500-12500 = 4000.

P+R = 10400.

R = 10400-4000 = 6400.

Q+R = 12500.

Q = 12500-6400 = 6100.

Nidhi said: (Aug 7, 2015)  
Thanks @Vinay.

Now I got it you have done the simplest way to solve.

You have a good explain ability.

Bhanu Ravali said: (Sep 3, 2015)  
P + Q + = 10100.

+ Q + R = 12500.

---------------

P + 2Q + R = 22600.

P + + R = 10400 (subtraction).

--------------

2Q = 12200.

Q = 6100.

P + Q = 10100.

P = 10100 - 6100.

= 4000.

Pranav said: (Apr 26, 2016)  
Think Logically.

Given Data:

P and Q = 5050.
Q and R = 6250.
P and R = 5200.

Solution:

Take common point = (Q and R) - (P and R).
(6250) - (5200) = 1050 -----> equation 1.

Now,
(P and Q) - (equation 1).
(5050) - (1050) = 4000.

So, the Answer is 4000.

Vipin said: (Jun 18, 2016)  
The quickest method is :

(p and q) + (p and r) - (q and r).
5050 + 52000 - 6250.
10250 - 6250.

Answer is = 4000.

Aman Dewangan said: (Jun 23, 2016)  
It can be solved directly:

(p+q) = (2*5050).....(1)
(p+r) = (2*5200).....(2)

We want to get value of p.

So,

Add eq (1 & 2)

=> 2p+(q+r) = 20500....(3)
=> As (q+r) = (2*6250) is given,

Put this in eq.(3).

2p = 20500-12500,
2p = 8000,
p = 4000.

Amani said: (Jun 28, 2016)  
Easily explained @Yesu Babu.

Pema Wangcan said: (Jul 14, 2016)  
Its simple, what we have to do is concentrate on what was the logic behind the question see.

They have already given the average of PQ =5050, QR=6250 and PR=5200. But we have to see the income of P only, therefore average means individual share for P he has 5050 + 5200 = 10250.
But see here. The share of P was shared by both R and Q which means P has to get his share. And we have to deduct 6250. (10250 - 6250) = 4000.

Kayalvizhi said: (Aug 27, 2016)  
p + Q = 5050
Q + R = 6250
P + R = 5200

(P + Q) - (Q + R) = 1200.

Now 5200 - 1200 = 4000.

I done like this is correct way or not?

Sam said: (Sep 15, 2016)  
Average of P and Q means (P + Q/2) = 5050.

Then it becomes, 2 goes that side.

P + Q = (5050 x 2) = 10100, Eq ---> (i).

Average of Q and R means Q + R/2.

Q + R = (6250 x 2) = 12500, Eq ---> (ii).

P + R/2.

P + R = (5200 x 2) = 10400, Eq ---> (iii).

Adding (i) , (ii) and (iii) , we get: 2 (P + Q + R) = 33000 or P + Q + R = 16500, Eq ---> (iv).

Subtracting (ii) from (iv), we get P = 4000.

P's monthly income = Rs. 4000.

Rechu said: (Sep 25, 2016)  
SIMPLY
P + Q + R = 16500.
P + 12500 = 16500.
P = 16500 - 12500.
P = 4000.

Asmara said: (Oct 9, 2016)  
Why we subtract total from equation (ii) as that is a monthly income of Q+R. How we can assume it's P's monthly income while there is No written P, Please explain.

Shiva Kumar said: (Apr 21, 2017)  
hi asmara

First avg income P+Q= 10100 {1}
Q+R= 12500 {2}
P+R= 10400 {3}

First adding eq 1 and 2 (P+Q)+(P+R) = 10100+10400 = 20500.
2P+Q+R= 20500 [4].
then subtract eq 4 and 2.
2P+Q+R-(Q+R ) = 20500-12500=8000.
2P =8000.
P = 4000.

Luciano said: (Jun 2, 2017)  
Why can't we take (5050+6250-5200)/2 = Q , Then use 5050 - Q = P?

Ravi said: (Jun 24, 2017)  
Superb, thanks @Praveen.

Santosh said: (Aug 2, 2017)  
It's very Simple firstly do addition were p is present in question and subtract to were p is absent. Like P and Q is 5050 then P and are is 5200 add both 5050+5200= 10,250 then subtract to Q and are is 6250 then your answer will be 4000.

Kalpana said: (Aug 7, 2017)  
Anyone can help me by solving this?

The average of a group of 13 members is 48 years. A member of the group age 57 retired and in place of him a new person aged 18 joined the group. Find the new average of the group.

Sadhya said: (Aug 11, 2017)  
first i tell the procedure @Kalpana.
13*48 = 624
57 - 18 = 39
so 624 - 39 = 585.
585\13 = 45 answer.

Or tricky method here average is 48 but the person who has 57 is retired that means 57 - 48 = 9 this is the number reduced.in addition to this in place of 48 only 18 joined that means there is a decrease of 30.

Finally, the decrease of average is 30 + 9 = 39. 39/13 =3 . so 48 - 3 = 45 answer.

Bhavna said: (Aug 29, 2017)  
Very nice way explanation thanks @Tarun.

Likhita said: (Sep 18, 2017)  
Thanks @Tarun it's very excellent explanation.

Kheyali Chanak said: (Nov 30, 2017)  
It will be simple if apply (i)- (ii)+(iii) then we get 2P=8000, therefore P=4000.

Subhankar said: (Jul 5, 2018)  
5050+5200=1025, 10250-6250=4000.

K L N Sarma said: (Aug 25, 2018)  
Guys, if you say p=4000, what will be your answers for Q and R.

My answer is p=2000, Q=3050, R = 3200
If we add all the 3 equations, we get 2 times (P+Q+R) = 16500. therefore, P+Q+R = 16500/2 = 8250.
8250 - (Q+R) = 8250-6250 = 2000.

Bhanu said: (Sep 1, 2018)  
Thank you @Prabhjeet.

Akhilesh said: (Sep 12, 2018)  
Thanks for the @Sai Kumar.

Dora said: (Oct 12, 2018)  
Add the values of ( PQ+PR) - QR ie;

By doing this the value of Q and R will be excluded from both PQ and PR.
= (5050+5200)-6250,
=10200-6250.
= 4000.

Kiran said: (Nov 20, 2018)  
Well said @Dora.

Raghavendra said: (Dec 31, 2018)  
@Praveen.

The initial step wrong.

P+q=5050.
Q+r=6250.
P+r=5200.
Each value should multiply with 2 as it was average, not individual.

Shahrukh said: (Jan 29, 2019)  
I don't know why the amount of q and are is being deducted?

P has two incomes 5050 and 5200. Why are the incomes of q and r is concerned with p? As it is cleared that p has these incomes. Question is about the income of p not about q and r.

Deepak Kumar Sharma said: (Apr 6, 2019)  
5050 + 5200 = 10250-6250 = 4000.

Dibyansh Pattanaik said: (Jul 4, 2019)  
@All.

1. Why we subtracted QR or Why we deducted QR?
2. What would be the solution if the monthly income of Q is asked?

Please, anyone, clarify it.

Sakshi Pandey said: (Jul 10, 2019)  
P + q= 5050*2=10100.
Q+r= 6250*2=12500.
P+r= 5200*4= 10400.

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

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