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

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Math Expert
Joined: 02 Sep 2009
Posts: 48037
Working continuously 24 hours a day, a factory bottles Soda Q at a rat  [#permalink]

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08 Jul 2018, 21:38
00:00

Difficulty:

85% (hard)

Question Stats:

39% (02:16) correct 61% (02:06) wrong based on 51 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, 23:03

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, 03:48
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 &nbs [#permalink] 09 Jul 2018, 03:48
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