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Working continuously 24 hours a day, a factory bottles Soda
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06 Jul 2018, 16:25
06 Jul 2018, 16:25
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Question Stats:
41% (02:37) correct
58% (02:30) wrong based on 90 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)\(\frac{10}{3}\)
(A)\(\frac{3}{10}\)
(B)\(\frac{5}{6}\)
(C)\(\frac{6}{5}\)
(D)\(\frac{8}{3}\)
(E)\(\frac{10}{3}\)
Re: Working continuously 24 hours a day, a factory bottles Soda
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07 Jul 2018, 17:43
07 Jul 2018, 17:43
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From question,
A factory bottles soda Q at the rate of 500 litres every second
or, \(500 * 3600\) litres every hr
or, \(500 * 3600 * 24\) litres every day
Let us assume that every bottle of soda Q is of \(500\) litres.
Hence no of bottles manufactured in the factory = \(\frac{500 * 3600 * 24}{500} = 86400\)
Soda V on the other hand is bottled at the rate of 300 litres every second
Therefore in 1 day total litres filled = \(300 * 24 * 3600\).
We know that the total numbers bottled must be twice the number of Soda Q bottle.
Therefore, we can form a eqn to find the volume of each bottle.
\(\frac{300 * 24 * 3600}{x} = 2 * 86400\)
or, \(3 * 24 * 3600 = 1728x\)
solving for \(x\) we get,
\(x = 150\)
Hence volume of soda Q = 500 while volume of soda V = 150
Ratio = \(\frac{500}{150} = \frac{50}{15} = \frac{10}{3}\)
A factory bottles soda Q at the rate of 500 litres every second
or, \(500 * 3600\) litres every hr
or, \(500 * 3600 * 24\) litres every day
Let us assume that every bottle of soda Q is of \(500\) litres.
Hence no of bottles manufactured in the factory = \(\frac{500 * 3600 * 24}{500} = 86400\)
Soda V on the other hand is bottled at the rate of 300 litres every second
Therefore in 1 day total litres filled = \(300 * 24 * 3600\).
We know that the total numbers bottled must be twice the number of Soda Q bottle.
Therefore, we can form a eqn to find the volume of each bottle.
\(\frac{300 * 24 * 3600}{x} = 2 * 86400\)
or, \(3 * 24 * 3600 = 1728x\)
solving for \(x\) we get,
\(x = 150\)
Hence volume of soda Q = 500 while volume of soda V = 150
Ratio = \(\frac{500}{150} = \frac{50}{15} = \frac{10}{3}\)
Re: Working continuously 24 hours a day, a factory bottles Soda
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10 Jul 2018, 06:17
10 Jul 2018, 06:17
4
Expert Reply
Explanation
If twice as many bottles of Soda V as of Soda Q are filled at the factory each day, then twice as many bottles of Soda V as of Soda Q are filled at the factory each second.
Use smart numbers for the number of bottles filled each second. Since twice as many bottles of Soda V are produced, the output in one second could be 100 bottles of Soda V and 50 bottles of Soda Q.
Using these numbers, the volume of the Q bottles is 500 liters ÷ 50 bottles = 10 liters per bottle and the volume of the V bottles is 300 liters ÷ 100 bottles = 3 liters per bottle. The ratio of the volume of a bottle of Q to a bottle of V is 10 liters ÷ 3 liters = \(\frac{10}{3}\).
If twice as many bottles of Soda V as of Soda Q are filled at the factory each day, then twice as many bottles of Soda V as of Soda Q are filled at the factory each second.
Use smart numbers for the number of bottles filled each second. Since twice as many bottles of Soda V are produced, the output in one second could be 100 bottles of Soda V and 50 bottles of Soda Q.
Using these numbers, the volume of the Q bottles is 500 liters ÷ 50 bottles = 10 liters per bottle and the volume of the V bottles is 300 liters ÷ 100 bottles = 3 liters per bottle. The ratio of the volume of a bottle of Q to a bottle of V is 10 liters ÷ 3 liters = \(\frac{10}{3}\).
