Working continuously 24 hours a day, a factory bottles Soda

BTGmoderatorLU wrote:Source: Manhattan Prep

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. 3/10
B. 5/6
C. 6/5
D. 8/3
E. 10/3

The OA is E

Since the question asks for the ratio and not the actual answer, we need not take 24 hours per day into consideration.

Ratio of Rate of filling Soda Q : Rate of filling Soda V :: 500 : 300 => 5 : 3.
Ratio of number of bottles of Soda Q : number of bottles of Soda V :: 2 : 1

Thus,

Ratio of the volume of a bottle of Soda Q to a bottle of Soda V = (5*2) : (3*1) = 10 : 3

Correct answer: E

Hope this helps.

-Jay
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BTGmoderatorLU wrote:Source: Manhattan Prep

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. 3/10
B. 5/6
C. 6/5
D. 8/3
E. 10/3

The OA is E

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

1000/q = 300/v

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

1000/300 = q/v

q/v = 10/3

Answer: E

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

Final Answer: E

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