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There are 4 bottles with the same number balls m respectively

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There are 4 bottles with the same number balls m respectively  [#permalink]

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New post Updated on: 24 Apr 2016, 11:24
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There are 4 bottles with the same number balls m respectively. If balls from only the 1-st bottle are moved to the other 3 bottles and finally the ratio of the numbers of balls in the bottles is 1 : 6 : 5 : 4, what fraction does the moved balls represent in terms of m?

A. m/4
B. m/2
C. 3m/4
D. m
E. 4m/5

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Originally posted by sairam595 on 24 Apr 2016, 05:58.
Last edited by Vyshak on 24 Apr 2016, 11:24, edited 1 time in total.
Edited the question for better understanding
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Re: There are 4 bottles with the same number balls m respectively  [#permalink]

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New post 09 Oct 2017, 03:22
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sairam595 wrote:
There are 4 bottles with the same number balls m respectively. If balls from only the 1-st bottle are moved to the other 3 bottles and finally the ratio of the numbers of balls in the bottles is 1 : 6 : 5 : 4, what fraction does the moved balls represent in terms of m?

A. m/4
B. m/2
C. 3m/4
D. m
E. 4m/5


All 4 bottles had the same number of marbles. The ratio became 1:6:5:4. Let's see if we can shave off some balls from the last three bottles and put them in the first to make them all have equal number of balls.

Since the last bottle has 4 balls (the least of the last three), let's give the extra balls of 2nd and 3rd bottles to the 1st bottle.

1+3 : 6 - 2 : 5 - 1 : 4

4 : 4 : 4 : 4

This is exactly what we want. So we removed 3 out of the 4 balls from the first bottle. So 3/4 of the balls were removed.

Answer (C)
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Re: There are 4 bottles with the same number balls m respectively  [#permalink]

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New post 24 Apr 2016, 11:11
Hi could u pls explain this with an algebraic approach? Thank you
chetan2u

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Re: There are 4 bottles with the same number balls m respectively  [#permalink]

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New post 24 Apr 2016, 11:18
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rahulkashyap wrote:
Hi could u pls explain this with an algebraic approach? Thank you
chetan2u

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Hi,

Quote:
There are 4 bottles with the same number balls m respectively. If balls from the only 1-st bottle are moved to the other 3 bottles and finally the ratio of the numbers of balls of the bottles is 1 to 6 to 5 to 4, does the moved balls represent in terms of m?

A. m/4 B. m/2 C. 3m/4 D. m E. 4m/5


what you have to realize is the Total number after distr would be the same as earlier..

now it is 1:6:5:4..
let the common ratio be x, then total number = (1+6+5+4)*x...
but earlier all were distributed equally among all four =\(\frac{16x}{4}=4x.\).
so m=4x OR \(x=\frac{m}{4}\).
what was the balls moved 4x-x=3x.. 4x was initial and present is 1*x
so \(3x = 3*\frac{m}{4} = \frac{3m}{4}\)
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There are 4 bottles with the same number balls m respectively  [#permalink]

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New post 23 Oct 2018, 08:19
sairam595 wrote:
There are 4 bottles with the same number balls m respectively. If balls from only the 1-st bottle are moved to the other 3 bottles and finally the ratio of the numbers of balls in the bottles is 1 : 6 : 5 : 4, what fraction does the moved balls represent in terms of m?

A. m/4
B. m/2
C. 3m/4
D. m
E. 4m/5


I wonder if this approach is correct

1 : 6 : 5 : 4 imagine there are 1, 6, 5 and 4 bottles after removing balla from the first one


    so bottle 1 has 1 ball
    bottle 2 has 6 balls (5 balls were moved into it)
    bottle 3 has 5 balls (4 balles were moved)
    bottle 4 has 4 balls (3 balls were moved)

Number of moved balls 5+4+3 =12
Total number of balls 16

Hence \(\frac{12}{16}\) = \(\frac{3}{4}\)

pushpitkc is my reasoning correct :)
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There are 4 bottles with the same number balls m respectively  [#permalink]

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New post 23 Oct 2018, 12:34
1
dave13 wrote:
sairam595 wrote:
There are 4 bottles with the same number balls m respectively. If balls from only the 1-st bottle are moved to the other 3 bottles and finally the ratio of the numbers of balls in the bottles is 1 : 6 : 5 : 4, what fraction does the moved balls represent in terms of m?

A. m/4
B. m/2
C. 3m/4
D. m
E. 4m/5


I wonder if this approach is correct

1 : 6 : 5 : 4 imagine there are 1, 6, 5 and 4 bottles after removing balla from the first one


    so bottle 1 has 1 ball
    bottle 2 has 6 balls (5 balls were moved into it)
    bottle 3 has 5 balls (4 balles were moved)
    bottle 4 has 4 balls (3 balls were moved)

Number of moved balls 5+4+3 =12
Total number of balls 16

Hence \(\frac{12}{16}\) = \(\frac{3}{4}\)

pushpitkc is my reasoning correct :)


Hi dave13

Unfortunately, the solution that you have used is wrong.

What's important to understand is that the number of balls is equal in each bottle
is the same, to begin with. All 4 bottles must have m balls each. Let that number be 4.

Now, that balls move from the first bottle to other 3 bottles and we need a ratio - 1:6:5:4

This will happen when 3 balls are moved from bottle 1 - 2 balls into bottle 2 and 1 ball into bottle 3.
Bottle 1: 4 - 3 = 1 | Bottle 2: 4 + 2 = 6 | Bottle 3: 4 + 1 = 5 | Bottle 4: 4 + 0 = 4 (Ratio - 1:6:5:4)

Therefore, the fraction of balls moved is 3m/4 as 3 balls are moved from Bottle 1(when m=4)

Hope that helps!
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Re: There are 4 bottles with the same number balls m respectively  [#permalink]

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New post 23 Oct 2018, 15:59
Hi,

The wording in this question was a bit confusing for me. Are we not supposed to assume all the balls were moved out of the 1st tube?
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Re: There are 4 bottles with the same number balls m respectively  [#permalink]

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New post 24 Oct 2018, 04:38
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bpdulog wrote:
Hi,

The wording in this question was a bit confusing for me. Are we not supposed to assume all the balls were moved out of the 1st tube?


No, even if you feel that perhaps all the balls were moved, you see that the given ratio is 1:6:5:4.
So some balls were certainly retained in the first bottle.
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Re: There are 4 bottles with the same number balls m respectively  [#permalink]

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New post 12 Nov 2018, 04:23
The final ratio is:......1:6:5:4 (which makes a total of 16 parts)

the first bottle has 1/16 of 4m balls remaining --> 4m/16 = m/4
this means the number of balls moved are: m - m/4 = 3m/4
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Re: There are 4 bottles with the same number balls m respectively   [#permalink] 12 Nov 2018, 04:23
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