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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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24 Apr 2016, 05:58
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35% (medium)

Question Stats:

76% (01:48) correct 24% (02:19) wrong based on 80 sessions

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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
[Reveal] Spoiler: OA

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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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Joined: 09 Oct 2015
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Re: There are 4 bottles with the same number balls m respectively [#permalink]

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

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Posts: 5721
Re: There are 4 bottles with the same number balls m respectively [#permalink]

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

Posted from my mobile device

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 $$3x = 3*\frac{m}{4} = \frac{3m}{4}$$
C
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Re: There are 4 bottles with the same number balls m respectively [#permalink]

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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.

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Re: There are 4 bottles with the same number balls m respectively   [#permalink] 09 Oct 2017, 03:22
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