Aptitude - Average - Discussion

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

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.

Average income of P & Q is 5050.
This means, P's average is 5050 & Q's average is 5050.
now, we can write P+Q => 5050 + 5050 = 10100 ----> 1

Similarly for Q and R average salary is 6250
hence, Q + R => 6250 + 6250 = 12500 ---> 2

Similarly for P and R average salary is 5200
hence, P + R => 5200 + 5200 = 10400 ---> 3

Adding all these equations, we get:
(P+Q)+(Q+R)+(P+R) => 10100+12500+10400 = 33000,
(P+Q)+(Q+R)+(P+R) can be written as 2(P+Q+R).

Hence, 2(P+Q+R) = 33000,
P + Q + R = 33000/2 = 16500.

we want P so:
P = 16500 - (Q+R),
P = 16500 - 12500 ( from 2),
P = 4000.

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

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

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.

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.

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.

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.

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.