Soda Q is bottled at a rate of 500 liters/second, 24 hours a day. Soda V is bottled at a rate of 300 liters/second, 24 hours a day. If twice as many bottles of Soda V as of Soda Q are filled in a day, what is the ratio of the volume of a bottle of Soda Q to a bottle of Soda V?

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slicergiza slicergiza · Answer 1 · 2019-07-30T13:16:42+02:00

Answer:

[tex]\frac{10}{3}[/tex]

Step-by-step explanation:

Let x be the filled bottles of soda Q,

As per statement,

The filled bottles of soda V = 2x,

Given,

Rate of filling of soda Q = 500 liters per sec,

So, the total volume filled by soda Q in a day = 500 × 86400 = 43200000 liters,

( ∵ 1 day = 86400 second ),

Thus, the volume of a bottle of Soda Q = [tex]\frac{\text{Total volume filled by soda Q}}{\text{filled bottles of soda Q}}[/tex]

[tex]=\frac{43200000}{x}[/tex]

Now, rate of filling of soda V = 300 liters per sec,

So, the total volume filled by soda V in a day = 300 × 86400 = 25920000 liters,

Thus, the volume of a bottle of Soda V

[tex]=\frac{25920000}{2x}[/tex]

Thus, the ratio of the volume of a bottle of Soda Q to a bottle of Soda V

[tex]=\frac{\frac{43200000}{x}}{\frac{25920000}{2x}}[/tex]

[tex]=\frac{10}{3}[/tex]