# Logical question

Experts
I have a question:
One person is having 3 houses.
the three tenants pay 25 per month.
The owner appoints a person A to collect the total rent .
A goes and gets 25+25+25=75
Now owner gives 5 to A.
A consumes 2 for cigerattes.
so remaining is 3 to A.
Now A returns 1 to each of the tenants .
so now tenants have actually given 24 to the owner(25 previously given and  1 returned by A)

Now let us do the resultant calculation:
Each tenant given 24.
So 24+24+24=72
A cosumed 2.
total 74.
But the Actually total collection was 75(total).

Where 1 Rs gone?
Thanking you
###### Who is Participating?

Commented:
Each tenant pays 25, making a total of 75
25 +25 +25 = 75

In this instance, they are given 1 back each meaning that they pay 24 each, a total of 72
24 (25-1) + 24 (25-1) + 24 (25-1) = 72

the owner only takes 70, leaving 2 for cigarettes for A
72 - 70 = 2

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Commented:
24+24+24=72
+ 3 given back = 75 given originally

24+24+24=72
- 2 A cosumed = 70 collected by owner

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Professional Troublemaker^h^h^h^h^hshooterCommented:
In the first case, the owner received 70 dollars (as (25+25+25) -5 (paid to agent).)
In the second case, the owner received 70 dollars (as (24+24+24) -2 (paid to agent).)
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Author Commented:
24+24+24=72 given by tenants
2 consumed by A
Total 74+2=74

But total should be 75.
This is question.

You have written
24+24+24=72
+ 3 given back = 75 given originally (from where 3 comes as A consumed 2)

Thanking you
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Commented:
You are adding the 2 to the 72, when you should be subtracting it from the 72
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Commented:
24+24+24=70+2

24+24+24+2 is no more relevant than 24+24+24+70
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Author Commented:
Expert  Razmux
you have written that
In the second case, the owner received 70 dollars (as (24+24+24) -2 (paid to agent).)

Now question is  (24+24+24) +2=74 but A originally collected 75.
why the total 74 is coming
Thanking you

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Commented:
Each tenant given 24.
So 24+24+24=72
Owner kept 70
total 142.
But the Actually total collection was 75(total).
Where 67 Rs gone?
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Professional Troublemaker^h^h^h^h^hshooterCommented:
> Now question is  (24+24+24) +2=74 but A originally collected 75.
> why the total 74 is coming

You shouldn't add 2 to the 72, you need to subtract 2, because that 2 went to the agent.
(And it matches what the owner originally received 70 (75 collected, less 5 to agent)
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Author Commented:
OZO

each tenant given only once not twice.(25+25+25)
A returned 1 to each of them. ok. so now how much the tenants given 25-1=24 (relatively consider)
Now A consumed 2
so calculation is coming as each tenant given 24  .
So total 72 given by tenants(relatively as actually previously they given 25 but later got 1 back)
A consumed 2
So where the 1 \$ goes?

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Commented:
each tenant given only once not twice.(25+25+25)
A returned 1 to each of them. ok. so now how much the tenants given 25-1=24 (relatively consider)
Now owner kept 70
so calculation is coming as each tenant given 24  .
So total 72 given by tenants(relatively as actually previously they given 25 but later got 1 back)
Owner kept 70
So where the 67 \$ goes?
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Author Commented:
The qeustion is not that------ how much the owner kept with him?

Rather In totallity you consider it as a system in which the money transfer is taking part .
But whatever may be the transfer the total collection was 75.
Who is getting what is immaterial .
Important is total can not shrink .
Here the total is shrinking ?
why?
see the total .Not individual how much getting.

Thanking you
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Commented:
Who is getting what is immaterial .
A consumes 2 for cigerattes. is immaterial
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progCommented:
credits and debits have been muddled, the credit of 5 to the collector has been forgotten

the collector has been credited with 80, he has been debited 3 for the refunds and 2 for the cigs - he is left with 75

you have added the tow he spent as a credit in error

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Author Commented:
this is a system in which
3 actors are there.
1.owner
2.A (collector)
3.Tenant

who is paying ?
tenants.
How much they payed 75

Now whatever is taking place afterwards is on that 75.
right.
so system is having 75\$
now money is transferred.
How?
A consumed 2\$.
given back to tenants 1 \$ to each tenants.
so each tenants are seeing that they have given 24 \$ as rent . since 1\$ is returned.

Now system's total is 75.
tenants given 24+24+24=72
right

2 \$ consumed by A.

System total 72+2=74

Previously what was system's total? 75.
How?
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Professional Troublemaker^h^h^h^h^hshooterCommented:
> Important is total can not shrink .

But what is ACTUALLY shrinking is the amount of money the agent is keeping... that total shrinks by 3.  If you wanted to add anything to the ( 24 x 3 = 72 ) collected from each tenant, you have to add THAT 3 to the 72 to get back to the 75.
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Author Commented:
deighton:

where from comes 80?
who paid 80?
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Commented:
tenants given 24+24+24=72
right
3 \$ returned
System total 72+3=75

Previously what was system's total? 75.
How?
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Author Commented:
ozo

you have written
3 \$ returned
who is returning 3\$?
and to whom?
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Commented:

who paid 80?
75 from tenants, 5 from owner
to A
=
75 to owner, 3 to tenants, 2 to cigarettes
from A
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Commented:
3 \$ returned
who is returning 3\$?
and to whom?

so remaining is 3 to A.
Now A returns 1 to each of the tenants .
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Author Commented:
OZO
if you want to say that tenants given tenants given 24+24+24=72
then 3 \$ returned  to tenants
then total is 75\$
then add 2\$ which A consumed
So the system total is now 77\$
How?
system can not have more.
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Commented:
if you want to say that tenants given tenants given 24+24+24=72
then 3 \$ returned  to tenants
then total is 75\$
then add 70\$ which owner kept
So the system total is now 145\$
How?
system can not have more.
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Author Commented:
OZO
is it possible that some one given you 75\$
and it has become 145\$?
how?
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Commented:
is it possible that some one given you 75\$
and it has become 74\$?
how?
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Author Commented:
Expert
that is my question as relatively it looks so .
But there must be some mistake in calculation of the totalling( That is while calculating the total of the system it is relatively looking as if the total is shrinking ).

Where is wrong ?
What is wrong in calculating the total?

This is the question.
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Commented:
(25-1)+(25-1)+(25-1)=25+25+25-3=70+2
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Commented:
What is wrong in calculating the total?
+2 should be -2
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Commented:
Just write it out, and things should make sense :

TENANT 1              TENANT 2                 TENANT 3                COLLECTOR (A)                 OWNER                 SHOP              TOTAL
starting condition :                                                    25                             25                                25                                   0                                         0                            0                      75
the three tenants pay 25 to A :                                 0                               0                                  0                                   75                                        0                            0                      75
A passes 70 to the owner, and keeps 5 :               0                               0                                  0                                    5                                        70                           0                      75
A consumes 2 for cigarettes :                                   0                               0                                  0                                    3                                        70                           2                      75
A returns 1 to each tenant :                                       1                               1                                  1                                    0                                        70                           2                      75

Notice how the total never changes ?
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Author Commented:
mattclarified

24 (25-1) + 24 (25-1) + 24 (25-1) = 72 is correct.
now you have written
leaving 2 for cigarettes for A
that is also correct.
so Previously system total was 75.
Now system total 74.
isn't it?
see the tenants have already paid.
that 75 \$ is only circulating.
Among 3 actors.
But when the total is being done it is not becoming 75

That is my question
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Commented:
this is because you keep adding the 2 to 72 when you should be taking it away, because only 70 was given to the owner.
72 + 2 for cigarettes = 74 is WRONG
72 - 2 for cigarettes = 70 is RIGHT
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Author Commented:
Infinity08:
your answer is absolutely correct as it shows the system total is not changing.

But can you do a bit of favour to me .

what is actually wrong in the following math

24*3=72+2=74 not equal to 75.
There is certainly a mistake  which I am not figuring out.
Thanking you
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Author Commented:
mattclarified
why
72 + 2 for cigarettes = 74 is WRONG
is wrong?
where is it wrong?
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Commented:
>> what is actually wrong in the following math
>>
>> 24*3=72+2=74 not equal to 75.

As others have tried to explain to you, you are adding the wrong values.

The value 72 consists of the 70 that the owner got, and the 2 that A consumed for cigarettes.
Instead of adding the price for the cigarettes to that value again, you should be adding the 3 that were distributed back among the tenants :

72 + 3 = 75
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Commented:

24*3=72+2=74 not equal to 75.
You are absolutely correct 74 = 75    but there is no reason that it should.
Your left hand side is WRONG
The net amount in from the rent is indeed 24*3 = 72
But where does that money go    70 to owner        net 2 to agent          72 = 72
- try again
money in   total rent    25*3   = 75
Where does money go     total 70 to owner     total 5 to agent         75 = 75
You CANNOT use net on one side of the equation and total on the other side.
If you change methods in the middle of the problem of course you get the wrong answer
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Commented:
This is a classic puzzle, my father showed it to me at least 50 years ago.

http://puzzles.nigelcoldwell.co.uk/twentyeight.htm

Nothing is missing.  Ever.  If you think there is you are confused.
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Author Commented:
Experts
It has been nice to have a discussion with you all.
Thanks for all the discussion.
Thanking you all,
Anindya Chatterjee
Bangalore
India
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