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V Ramachandran ...
Joined: 02 Feb 2009 Posts: 137 Location: Bangalore

Posted: Mon Jun 20, 2011 5:58 pm Post subject: How many MANGOES each one will get ? 


Mr. Pawar,
Are you asking a question, or is it a test for others?
In any case the answer is as follows. (Answer  Total mangoes plucked = 9)
Let the total no. of mangoes be = x
The first boy gets, x/3 mangoes, leaving a balance of 2x/3 mangoes.
The second boy divides this into 3 & takes one extra: He gets, (1/3)*( 2x/3 ) +1= (2x/9)+ 1 = the first boys share ie x/3 Equate these and solve for x
x/3 = 2x/9 + 1 ==> 3x = 2x + 9. ===> x=9 ==> Each boy gets 3 mangoes.
Simple maths!
Ramachandran.
From: sspawar <forum@sefindia.org>
To: speakout@sefindia.org
Sent: Mon, June 20, 2011 8:15:28 PM
Subject: [Speak Out] How many MANGOES each one will get ?
Three boys make a plan to steal
mangoes from a garden. One climbs over the tree. Second one shows him the good mango inside of Leaves and branches. Third one keeps watch over watchman and collect the dropped MANGOES. Suddenly he sees a watchman, may see them. Soon he does 3 equal share of dropped MANGOES and goes away taking one part. Second boy also makes 3 equal share of remained amount and find one balance. He takes one share and balance one also and runs away. Last one also gets success to carry remained MANGOES and runs away. Later they meet a place and find that they all have equal share. Can you give the number how much each one gets from? What are the equations?
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sspawar ...
Joined: 05 Jun 2009 Posts: 1175

Posted: Tue Jun 21, 2011 3:22 am Post subject: 


Dear Sir V Ramchandarn,
Your approach is correct but a little mistake is there.
Answer in other post is already given that is 2+2+2 = 6,
But Er. Abhio'expression in that post is hypothetic.
we can form such many equations , like wise of "x+1 = 2x" if 2x is each share.
for example :
x+2 = 2x, if x is share.
2x + 2 = 3x, if x is share.
now may be multiple of this, but these are not logical, no base, not explanable with the problem conditions.
By a sense it is clear that answer should be multiple of 3, because it is being divided in 3 equal share.
Now try for 3,6,9,and so on
by hit and trial,
Answer 6 is fit to the conditions, but answer 9 is incorrect.
(Readers himself may examine)

Another question framed of similar pattern (self made) 
Three boys make a plan to steal mangoes from a garden.
One climbs over the tree.
Second one shows him the good mango inside of Leaves and branches.
Third one keeps watch over watchman and collect the dropped MANGOES.
Suddenly he sees that a watchman may see them. Soon he does 3 equal share of dropped MANGOES and escapes away taking one share.
Second boy also sees a little later, and he find that 3rd boy already escaped away hence he makes again 3 equal share of remained amount of mangoes and while doing equal 3 shares, he finds 2 mangoes balance.
He takes one share and balance 2 mangoes also and runs away.
Last one also gets success to carry remained MANGOES and runs away.
Later they meet at a place and find that they all have equal numbers of mangoes.
Can you give the number how much each one gets from?
What are the equations?
Regards


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Raghuveer Shenoy Guest

Posted: Tue Jun 21, 2011 6:09 am Post subject: How many MANGOES each one will get ? 


Hello Sir,
The total number of mangoes are6
each one will take2
Assume Total number of mangoes=y
first person took y/3 mangoes
second person take ((x/3)+1)mangoes where x=2y/3
equate 1 & 2 , becoz both should be equal
similarly with 2 & third equation
we get total mangoes=6
each one take 2 mangoes
Raghuveer K S
98453 96592
Have a good day
From: V Ramachandran <forum@sefindia.org>
To: speakout@sefindia.org
Sent: Tue, June 21, 2011 4:10:59 AM
Subject: [Speak Out] Re: How many MANGOES each one will get ?
Mr. Pawar,
Are you asking a question, or is it a test for others?
In any case the answer is as follows. (Answer  Total mangoes plucked = 9)
Let the total no. of mangoes be = x
The first boy gets, x/3 mangoes, leaving a balance of 2x/3 mangoes.
The second boy divides this into 3 & takes one extra: He gets, (1/3)*( 2x/3 ) +1= (2x/9)+ 1 = the first boys share ie x/3 Equate these and solve for x
x/3 = 2x/9 + 1 ==> 3x = 2x + 9. ===> x=9 ==> Each boy gets 3 mangoes.
Simple maths!
Ramachandran.
From: sspawar
To: speakout@sefindia.org (speakout@sefindia.org)
Sent: Mon, June 20, 2011 8:15:28 PM
Subject: [Speak Out] How many MANGOES each one will get ?
Three boys make a plan to steal
mangoes from a garden. One climbs over the tree. Second one shows him the good mango inside of Leaves and branches. Third one keeps watch over watchman and collect the dropped MANGOES. Suddenly he sees a watchman, may see them. Soon he does 3 equal share of dropped MANGOES and goes away taking one part. Second boy also makes 3 equal share of remained amount and find one balance. He takes one share and balance one also and runs away. Last one also gets success to carry remained MANGOES and runs away. Later they meet a place and find that they all have equal share. Can you give the number how much each one gets from? What are the equations?
Treat yourself at a restaurant, spa, resort and much more with Rediff]http://track.rediff.com/click?url=___http://dealhojaye.rediff.com?sc_cid=mailsignature___&cmp=signature&lnk=rediffmailsignature&newservice=deals]Rediff Deal ho jaye!
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n.krishnaprasad SEFI Member
Joined: 19 Nov 2010 Posts: 3

Posted: Tue Jun 21, 2011 4:29 pm Post subject: How many MANGOES each one will get ? 


Seems wrong just check.
 On Mon, 6/20/11, V Ramachandran <forum@sefindia.org> wrote:
Quote: 
From: V Ramachandran <forum@sefindia.org>
Subject: [Speak Out] Re: How many MANGOES each one will get ?
To: speakout@sefindia.org
Date: Monday, June 20, 2011, 10:40 PM
Mr. Pawar,
Are you asking a question, or is it a test for others?
In any case the answer is as follows. (Answer  Total mangoes plucked = 9)
Let the total no. of mangoes be = x
The first boy gets, x/3 mangoes, leaving a balance of 2x/3 mangoes.
The second boy divides this into 3 & takes one extra: He gets, (1/3)*( 2x/3 ) +1= (2x/9)+ 1 = the first boys share ie x/3 Equate these and solve for x
x/3 = 2x/9 + 1 ==> 3x = 2x + 9. ===> x=9 ==> Each boy gets 3 mangoes.
Simple maths!
Ramachandran.
From: sspawar
To: speakout@sefindia.org (speakout@sefindia.org)
Sent: Mon, June 20, 2011 8:15:28 PM
Subject: [Speak Out] How many MANGOES each one will get ?
Three boys make a plan to steal
mangoes from a garden. One climbs over the tree. Second one shows him the good mango inside of Leaves and branches. Third one keeps watch over watchman and collect the dropped MANGOES. Suddenly he sees a watchman, may see them. Soon he does 3 equal share of dropped MANGOES and goes away taking one part. Second boy also makes 3 equal share of remained amount and find one balance. He takes one share and balance one also and runs away. Last one also gets success to carry remained MANGOES and runs away. Later they meet a place and find that they all have equal share. Can you give the number how much each one gets from? What are the equations?
Treat yourself at a restaurant, spa, resort and much more with Rediff Deal ho jaye!

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sspawar ...
Joined: 05 Jun 2009 Posts: 1175

Posted: Wed Jun 22, 2011 4:35 am Post subject: Re: How many MANGOES each one will get ? 


Dear Er. Krishnaprasad,
Yes equation or expressions given by Mr. Sahay is wrong .
Because (2y/9) +1 = y/3 => will give ans Y =9, while ans is 6 hence wrong.
Answer 9 is also incorrect because After taking 1st share =3nos by 1st boy, when second will divide remaining =6nos, in 3 parts it will be equally dividable = 2x3 =6 and balance one will not be there.hence 9 ans is wrong.
Regards
n.krishnaprasad wrote:  Seems wrong just check.
 On Mon, 6/20/11, V Ramachandran <forum> wrote:
Quote: 
From: V Ramachandran <forum>
Subject: [Speak Out] Re: How many MANGOES each one will get ?
To: speakout@sefindia.org
Date: Monday, June 20, 2011, 10:40 PM
Mr. Pawar,
Are you asking a question, or is it a test for others?
In any case the answer is as follows. (Answer  Total mangoes plucked = 9)
Let the total no. of mangoes be = x
The first boy gets, x/3 mangoes, leaving a balance of 2x/3 mangoes.
The second boy divides this into 3 & takes one extra: He gets, (1/3)*( 2x/3 ) +1= (2x/9)+ 1 = the first boys share ie x/3 Equate these and solve for x
x/3 = 2x/9 + 1 ==> 3x = 2x + 9. ===> x=9 ==> Each boy gets 3 mangoes.
Simple maths!
Ramachandran.
From: sspawar
To: speakout@sefindia.org (speakout@sefindia.org)
Sent: Mon, June 20, 2011 8:15:28 PM
Subject: [Speak Out] How many MANGOES each one will get ?
Three boys make a plan to steal

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atul_123 ...
Joined: 29 May 2009 Posts: 369

Posted: Wed Jun 22, 2011 11:52 am Post subject: 


here i think i want to give ans as per my approach.
say total
MANGOES are 3x
first boy take 3x/3=x nos with him.
remaining
MANGOES are 2x
second boy divide it in 3, say he got y part each and find one extra MANGO and take so say that he take y + 1
and third boy take remaining 2y part
now as per starting total
MANGOES
are 3x
so total sum of three boys part is
x + (y+1) + (2y) = 3x .............................................. (1)
as per equation all have taken same nos so second boy take same as first boy so
y + 1 = x
so y = x  1
so replace y by x  1 in eq 1
x + ( (x  1) + 1 ) + 2 ( x  1 ) = 3x
x + x  1 + 1 + 2x  2 = 3x
4x  2 = 3x
4x  3x = 2
so x = 2
so total nos of
MANGOES are 3x = 3 * 2 = 6
i think it is right approach....


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sspawar ...
Joined: 05 Jun 2009 Posts: 1175

Posted: Wed Jun 22, 2011 3:35 pm Post subject: 


Dear Atul and all,
Yes you are correct. you proved mathematically.
But Logically you still away from the core bit of this problem.
Your solution is like that you have won title of the cricket match by Duckworth lewis method, but not clear cut.
You have given check the king of Chess, but not get him surrendered.
If it is any laughter show  you are getting 9 marks of course but not 10.
let we see
All 3 gets equal hence say = X each.
Hence total = 3X,
Now 1st gets = X  Eq 1
Now second receives 2X but while dividing it in 3 parts he gets 3 equal parts +1
Means = [(2X  1) /3] + [(2X  1) /3]+ [(2X  1) /3]+1,
(here every body was committing mistake by doing = (2x/3) +1 this is the wrong expression, and this is turning point of this question)
Thus Second will get as per condition given = [(2X  1) /3] +1  Eq 2
Third will get = 2(2X  1) /3  Eq 3
Equate all 3.
X = [(2X  1) /3] +1 = 2(2X  1) /3
Now solve any 2 eq will give X =2

Thanks
atul_123 wrote:  here i think i want to give ans as per my approach.
say total
MANGOES are 3x
first boy take 3x/3=x nos with him.
remaining
MANGOES are 2x
second boy divide it in 3, say he got y part each and find one extra MANGO and take so say that he take y + 1
and third boy take remaining 2y part
now as per starting total
MANGOES
are 3x
so total sum of three boys part is
x + (y+1) + (2y) = 3x .............................................. (1)
as per equation all have taken same nos so second boy take same as first boy so
y + 1 = x
so y = x  1
so replace y by x  1 in eq 1
x + ( (x  1) + 1 ) + 2 ( x  1 ) = 3x
x + x  1 + 1 + 2x  2 = 3x
4x  2 = 3x
4x  3x = 2
so x = 2
so total nos of
MANGOES are 3x = 3 * 2 = 6
i think it is right approach.... 
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V Ramachandran ...
Joined: 02 Feb 2009 Posts: 137 Location: Bangalore

Posted: Wed Jun 22, 2011 6:20 pm Post subject: How many MANGOES will each one get ? 


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Dear Friends,
I seem to have misunderstood the problem. I am giving the calculations in both the cases: I have also located the mistake.
Case 1 (9 mangoes) Case 2 (6 mangoes)
1. First boy sees (y ) 9 6
2. He takes 3 2
3. Balance (x) 6 4
4. Boy 2 takes (x/3)+1 2+1=3 (4/3) +1 = 2.1/3 not 2
5. Balance now for boy 3 3 1.2/3
The key word is: the second boy makes 3 equal shares of remaining mangoes and "finds one balance”
In my calculations I have not accounted for the balance – which I have missed! The calculations are involving only integers, which means it has to be by trial & error method! Not “simple maths” as I remarked!
Thanks for the fun!
Best wishes,
V. Ramachandran.
From: Raghuveer Shenoy <forum@sefindia.org>
To: speakout@sefindia.org
Sent: Wed, June 22, 2011 9:11:20 AM
Subject: [Speak Out] Re: How many MANGOES each one will get ?
Hello Sir,
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atul_123 ...
Joined: 29 May 2009 Posts: 369

Posted: Fri Jun 24, 2011 6:05 am Post subject: 


sspawar wrote:  Dear Atul and all,
Yes you are correct. you proved mathematically.
But Logically you still away from the core bit of this problem.
Your solution is like that you have won title of the cricket match by Duckworth lewis method, but not clear cut.
You have given check the king of Chess, but not get him surrendered.
If it is any laughter show  you are getting 9 marks of course but not 10.
let we see
All 3 gets equal hence say = X each.
Hence total = 3X,
Now 1st gets = X  Eq 1
Now second receives 2X but while dividing it in 3 parts he gets 3 equal parts +1
Means = [(2X  1) /3] + [(2X  1) /3]+ [(2X  1) /3]+1,
(here every body was committing mistake by doing = (2x/3) +1 this is the wrong expression, and this is turning point of this question)
Thus Second will get as per condition given = [(2X  1) /3] +1  Eq 2
Third will get = 2(2X  1) /3  Eq 3
Equate all 3.
X = [(2X  1) /3] +1 = 2(2X  1) /3
Now solve any 2 eq will give X =2

Thanks
atul_123 wrote:  here i think i want to give ans as per my approach.
say total
MANGOES are 3x
first boy take 3x/3=x nos with him.
remaining
MANGOES are 2x
second boy divide it in 3, say he got y part each and find one extra MANGO and take so say that he take y + 1
and third boy take remaining 2y part
now as per starting total
MANGOES
are 3x
so total sum of three boys part is
x + (y+1) + (2y) = 3x .............................................. (1)
as per equation all have taken same nos so second boy take same as first boy so
y + 1 = x
so y = x  1
so replace y by x  1 in eq 1
x + ( (x  1) + 1 ) + 2 ( x  1 ) = 3x
x + x  1 + 1 + 2x  2 = 3x
4x  2 = 3x
4x  3x = 2
so x = 2
so total nos of
MANGOES are 3x = 3 * 2 = 6
i think it is right approach.... 

dear Mr. Pawar,
to make ans short i have written that ans.
but after first boy had divided MANGOES in 3 part he take x and left 2x.
second boy take y+1 and third boy take 2y
so (y+1) + (2y) = 2x
so 3y + 1 = 2x
so 3y = 2x  1
so y = (2x  1) / 3 ..................2
so second boy = y + 1 = (((2x  1) / 3) + 1) as per EQ 2
and third boy = 2y = 2 (( 2x  1) / 3) EQ 3
and total is 3x = x + (((2x  1) / 3) + 1) + 2 ( ((2x  1) / 3)
and solution as you have shown....
as per your EQ 2 and EQ 3 i got EQ 2 & EQ 3
i am admitting that i have gone for short method to complete my ans in short,
and also thanks to for that kind of puzzle to make our mind sharp...
if you have more than post.


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