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At the start of the day the amount of water in two identical buckets

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Math Expert
Joined: 02 Sep 2009
Posts: 44651
At the start of the day the amount of water in two identical buckets [#permalink]

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28 Dec 2017, 21:45
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Question Stats:

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At the start of the day the amount of water in two identical buckets is 3 liters in bucket A and 2 liters in bucket B. If x liters are then added to A and 4x liters are added to B so that the ratio of A to B is 3 to 10, how much water has been added to bucket B?

A. 4 liter
B. 12 liters
C 16 liters
D. 48 liters
E. 72 liters
[Reveal] Spoiler: OA

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Joined: 18 Aug 2016
Posts: 631
Re: At the start of the day the amount of water in two identical buckets [#permalink]

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29 Dec 2017, 06:04
Bunuel wrote:
At the start of the day the amount of water in two identical buckets is 3 liters in bucket A and 2 liters in bucket B. If x liters are then added to A and 4x liters are added to B so that the ratio of A to B is 3 to 10, how much water has been added to bucket B?

A. 4 liter
B. 12 liters
C 16 liters
D. 48 liters
E. 72 liters

A:B::3:2
A:B::3+x:2+4x = 3:10

30+10x = 6+12x
2x=24
x=12
4x was added to bucket b = 4*12 = 48
D
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Luckisnoexcuse

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Joined: 28 Dec 2017
Posts: 31
Re: At the start of the day the amount of water in two identical buckets [#permalink]

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29 Dec 2017, 10:55
(3 + x) / (2 + 4x) = 3 / 10 (because of A to B ratio)

Cross-multiplying gives 30 + 10x = 6 + 12x
Solving for x gives us, x = 12

Since 4x liters was added to bucket B, 4*12 = 48 liters (answer D)
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Joined: 22 May 2016
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At the start of the day the amount of water in two identical buckets [#permalink]

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29 Dec 2017, 15:57
Bunuel wrote:
At the start of the day the amount of water in two identical buckets is 3 liters in bucket A and 2 liters in bucket B. If x liters are then added to A and 4x liters are added to B so that the ratio of A to B is 3 to 10, how much water has been added to bucket B?

A. 4 liter
B. 12 liters
C 16 liters
D. 48 liters
E. 72 liters

This question changes what we normally see, but solving it is done similarly.

Usually there is a given original ratio with a multiplier, and quantities to be added or subtracted that yield a new ratio.

Neither ratio here "takes" the multiplier. Instead, in the arithmetic, the multiplier accompanies the amounts added.

Original ratio: $$\frac{A}{B} = \frac{3}{2}$$

Add x liters to A and 4x liters to B, to yield a new ratio
$$\frac{3 + x}{2 + 4x}=\frac{3}{10}$$

$$3(2 + 4x) = 10(3 + x)$$
$$6 + 12x = 30 + 10x$$
$$2x = 24$$
$$x = 12$$

How much water was added to B?
This time the multiplier corresponds with amounts added.

B got 4x liters of water
x = 12
4x = 48 liters

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At the start of the day the amount of water in two identical buckets   [#permalink] 29 Dec 2017, 15:57
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