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# Working continuously 24 hours a day, a factory bottles Soda Q at a rat

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Working continuously 24 hours a day, a factory bottles Soda Q at a rat  [#permalink]

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08 Jul 2018, 20:38
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:25) correct 46% (02:28) wrong based on 177 sessions

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Working continuously 24 hours a day, a factory bottles Soda Q at a rate of 500 liters per second and Soda V at a rate of 300 liters per second. If twice as many bottles of Soda V as of Soda Q are filled at the factory each day, what is the ratio of the volume of a bottle of Soda Q to a bottle of Soda V?

(A) $$\frac{3}{10}$$

(B) $$\frac{5}{6}$$

(C) $$\frac{6}{5}$$

(D) $$\frac{8}{3}$$

(E) $$\frac{10}{3}$$

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Re: Working continuously 24 hours a day, a factory bottles Soda Q at a rat  [#permalink]

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08 Jul 2018, 22:03

Solution

Given:
• Working continuously 24 hours a day, a factory bottles Soda Q at a rate of 500 liters per second and Soda V at a rate of 300 liters per second
• Twice as many bottles of Soda V as of Soda Q are filled at the factory each day

To find:
• The ratio of the volume of a bottle of Soda Q to a bottle of Soda V

Approach and Working:
We assume that,
• Number of bottles of Soda Q = n
• Number of bottles of Soda V = 2n

Therefore, we can write:
• Volume of Soda per bottle of Q = V1 = $$\frac{500 * 3600 * 24}{n}$$
• Volume of Soda per bottle of V = V2 = $$\frac{300 * 3600 * 24}{2n}$$

Hence, the ratio V1: V2 = $$\frac{500 * 3600 * 24}{n}: \frac{300 * 3600 * 24}{2n}$$ = 500: 150 = 10: 3

Hence, the correct answer is option E.

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Re: Working continuously 24 hours a day, a factory bottles Soda Q at a rat  [#permalink]

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09 Jul 2018, 02:48
1
Bunuel wrote:
Working continuously 24 hours a day, a factory bottles Soda Q at a rate of 500 liters per second and Soda V at a rate of 300 liters per second. If twice as many bottles of Soda V as of Soda Q are filled at the factory each day, what is the ratio of the volume of a bottle of Soda Q to a bottle of Soda V?

Because we are computing ratio of the volumes of the two types of bottles, whether we find it for 24 hours or 1 second, the answer will the same.

Let the number of bottles of soda Q bottled every second be 'n'
So, the number of bottles of soda V bottled every second will be '2n'

Each second 500 litres of soda Q are bottled.
If in each second 'n' bottles of soda Q are bottled, volume of each bottle of soda Q = $$\frac{500}{n}$$ litres. ---- (1)

Each second 300 litres of soda V are bottled.
Each second '2n' bottles of soda V are bottled.
So, volume of each bottle of soda V = $$\frac{300}{2n} = \frac{150}{n}$$ litres. ---- (2)

Answer to question ratio of (1) and (2)
= $$\frac{500}{n}$$/$$\frac{150}{n}$$
= $$\frac{500}{n} * \frac{n}{150}$$
= $$\frac{500}{150} = \frac{10}{3}$$

Choice E
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Re: Working continuously 24 hours a day, a factory bottles Soda Q at a rat  [#permalink]

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01 Oct 2018, 11:58
Bunuel wrote:
Working continuously 24 hours a day, a factory bottles Soda Q at a rate of 500 liters per second and Soda V at a rate of 300 liters per second. If twice as many bottles of Soda V as of Soda Q are filled at the factory each day, what is the ratio of the volume of a bottle of Soda Q to a bottle of Soda V?

(A) $$\frac{3}{10}$$

(B) $$\frac{5}{6}$$

(C) $$\frac{6}{5}$$

(D) $$\frac{8}{3}$$

(E) $$\frac{10}{3}$$

$$Q:\,\,\,\,\frac{{500\,\,{\text{liters}}}}{{1\,\,{\text{second}}}}\,\,\,\,\,\,\,;\,\,\,\,\,\,\frac{{k\,\,{\text{bottles}}}}{{\left( {{\text{any}}\,\,{\text{time}}\,\,{\text{fixed,}}\,\,{\text{say}}} \right)\,\,\,\,1\,\,\,{\text{second}}}}$$

$$V:\,\,\,\,\frac{{300\,\,{\text{liters}}}}{{1\,\,{\text{second}}}}\,\,\,\,\,\,\,;\,\,\,\,\,\,\frac{{2k\,\,{\text{bottles}}}}{{\left( {{\text{same}}\,\,{\text{time}}\,\,{\text{fixed}}} \right)\,\,\,\,1\,\,\,{\text{second}}}}$$

(We could explore a particular case, say k=1, it doesn´t matter. We left "k" so that you will have a "better feeling" of the whole structure!)

$$? = \frac{{{\text{volume}}\,\,{\text{bottle}}\,\,Q}}{{{\text{volume}}\,\,{\text{bottle}}\,\,V}}$$

Let´s use UNITS CONTROL, one of the most powerful tools of our method!

$$Q:\,\,\,\,\,\,\,\frac{{500\,\,{\text{liters}}}}{{1\,\,{\text{second}}}}\,\,\,\left( {\frac{{1\,\,\,{\text{second}}}}{{\,k\,\,{\text{bottles}}\,}}\,\,\begin{array}{*{20}{c}} \nearrow \\ \nearrow \end{array}} \right)\,\,\, = \,\,\,\frac{{500\,\,\,{\text{liters}}}}{{k\,\,\,{\text{bottles}}}} = \frac{{\frac{{500}}{k}\,\,\,{\text{liters}}}}{{1\,\,\,{\text{bottle}}}}$$

$$V:\,\,\,\,\,\,\,\frac{{300\,\,{\text{liters}}}}{{1\,\,{\text{second}}}}\,\,\,\left( {\frac{{1\,\,\,{\text{second}}}}{{\,2k\,\,{\text{bottles}}\,}}\,\,\begin{array}{*{20}{c}} \nearrow \\ \nearrow \end{array}} \right)\,\,\, = \,\,\,\frac{{300\,\,\,{\text{liters}}}}{{2k\,\,\,{\text{bottles}}}} = \frac{{\frac{{150}}{k}\,\,\,{\text{liters}}}}{{1\,\,\,{\text{bottle}}}}$$

Obs.: arrows indicate licit converters.

$$? = \frac{{\,\,\,\frac{{500}}{k}\,\,\,}}{{\frac{{150}}{k}}} = \frac{{50}}{{15}} = \frac{{10}}{3}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Working continuously 24 hours a day, a factory bottles Soda Q at a rat  [#permalink]

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01 Oct 2018, 21:42
Hi All,

We're told that working continuously 24 hours a day, a factory bottles Soda Q at a rate of 500 liters per second and Soda V at a rate of 300 liters per second and that TWICE as many bottles of Soda V as of Soda Q are filled at the factory each day. We're asked for the ratio of the volume of a bottle of Soda Q to a bottle of Soda V. This question is all about ratios, so you can approach the math in a variety of different ways. You might also find it useful to TEST VALUES.

The fact that this scenario takes place in a 24-hour day is actually irrelevant to the math involved. Since the number of bottles created is an unknown, we can TEST VALUES to define the overall ratios involved.

IF... 1 bottle of Soda Q is created each second, then 2 bottles of Soda V are created each second.
Thus, 1 bottle of Soda Q is 500 liters and the 2 bottle of Soda V TOTAL 300 liters (meaning that each bottle is 300/2 = 150 liters).

The ratio of a bottle of Soda Q to a bottle of Soda V = 500:150 = 500/150 = 10/3

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Working continuously 24 hours a day, a factory bottles Soda Q at a rat  [#permalink]

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02 Oct 2018, 07:11
Different way of looking at this problem:

The ratio of liters per day will alwys be $$\frac{Q}{V} = \frac{5}{3}$$.

Lets assume there are only $$5$$ liters of $$Q$$ and $$3$$ liters of $$V$$. To make things easier lets use the LCM as the number of bottles of $$Q$$.

So $$15$$ bottles of $$Q$$, therefore $$30$$ bottles of $$V$$.

Liters per bottle for $$Q$$: $$\frac{5}{15}$$ $$-->$$ $$\frac{1}{3}$$

Liters per bottle for $$V$$: $$\frac{3}{30}$$ $$-->$$ $$\frac{1}{10}$$

Ratio bottles volume $$Q:V$$ -->$$\frac{1}{3}/\frac{1}{10}$$ $$-->$$ $$\frac{1}{3}*\frac{10}{1}$$ $$-->$$ $$\frac{10}{3}$$
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Re: Working continuously 24 hours a day, a factory bottles Soda Q at a rat  [#permalink]

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03 Oct 2018, 16:41
Bunuel wrote:
Working continuously 24 hours a day, a factory bottles Soda Q at a rate of 500 liters per second and Soda V at a rate of 300 liters per second. If twice as many bottles of Soda V as of Soda Q are filled at the factory each day, what is the ratio of the volume of a bottle of Soda Q to a bottle of Soda V?

(A) $$\frac{3}{10}$$

(B) $$\frac{5}{6}$$

(C) $$\frac{6}{5}$$

(D) $$\frac{8}{3}$$

(E) $$\frac{10}{3}$$

Let the volume of a bottle of Soda Q be q and the volume of a bottle of Soda V be v. Note that if twice as many bottles of Soda V are filled each day, the same must be true for the number of bottles filled each second; so we will compare those quantities instead.

In one second, 500/q bottles of Soda Q and 300/v bottles of Soda V are filled. Thus, we can create the equation:

2 x 500/q = (300/v)

Multiplying both sides of the equation by q/300, we have:

1000/300 = q/v

q/v = 10/3

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Re: Working continuously 24 hours a day, a factory bottles Soda Q at a rat   [#permalink] 03 Oct 2018, 16:41
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