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During a certain month, 40 percent of all the oil used by a certain fa

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yrozenblum
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During a certain month, 40 percent of all the oil used by a certain fa [#permalink] New post   Updated on: 14 Oct 2023, 11:11
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During a certain month, 40 percent of all the oil used by a certain factory was used by the oil heater. The cost per gallon of the oil used by the oil heater was half the cost per gallon of the rest of the oil used by the factory. For that month, the cost of the oil used by the oil heater was what fraction of the cost of all the oil used by the factory?

A. \(\frac{1}{6}\)

B. \(\frac{1}{5}\)

C. \(\frac{1}{4}\)

D. \(\frac{1}{3}\)

E. \(\frac{1}{2}\)
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C

Originally posted by yrozenblum on 14 Oct 2023, 10:40.
Last edited by gmatophobia on 14 Oct 2023, 11:11, edited 1 time in total.
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Re: During a certain month, 40 percent of all the oil used by a certain fa [#permalink] New post   14 Oct 2023, 11:16
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yrozenblum wrote:
During a certain month, 40 percent of all the oil used by a certain factory was used by the oil heater. The cost per gallon of the oil used by the oil heater was half the cost per gallon of the rest of the oil used by the factory. For that month, the cost of the oil used by the oil heater was what fraction of the cost of all the oil used by the factory?

A. \(\frac{1}{6}\)

B. \(\frac{1}{5}\)

C. \(\frac{1}{4}\)

D. \(\frac{1}{3}\)

E. \(\frac{1}{2}\)


During a certain month, 40 percent of all the oil used by a certain factory was used by the oil heater.

Assume in that given month 100 gallon of oil was used.

  • Oil used by Oil Heaters = 40 gallons
  • Oil used by Other Heaters = 60 gallons

The cost per gallon of the oil used by the oil heater was half the cost per gallon of the rest of the oil used by the factory.

Assume

  • Cost of per gallon oil used by Oil Heaters = $1
  • Cost of per gallon used by other Heaters = $2

For that month, the cost of the oil used by the oil heater was what fraction of the cost of all the oil used by the factory?

  • Cost of Oil used by Oil Heaters = 40 * $1 = $40
  • Cost of Oil used by Other Heaters = 60 * $2 = $120

Required Ratio = \(\frac{40}{40+120} = \frac{40}{160} = \frac{1}{4}\)

Option C
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Re: During a certain month, 40 percent of all the oil used by a certain fa [#permalink] New post   05 Mar 2024, 11:24
Let total Oil used be 100, and cost per unit of oil be $1

Cost for Oil heater = 40 * 1/2 = $20
Cost used by other equipment = 60 * 1 = $60

Ratio of costs is 20:60

Fraction of the cost of Oil heater's usage of oil = 20/80
Simplify this to get = 1/4
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Re: During a certain month, 40 percent of all the oil used by a certain fa [#permalink] New post   06 May 2024, 01:40
­let A = total oil

so oil used by oil heater = 0.4A
\(\\
\frac{Total cost of Oil used by oil heater}{0.4A} = \frac{1}{2}*\frac{total remaining oil cost}{ 0.6A}\\
\\
Cost Oil heater = \frac{1}{3}* Cost Remaining\\
\\
or 3*(C0st Oil Heater) = 1 * Cost Remaining\\
\\
\frac{Cost Oil}{Total Cost} = \frac{cost Oil }{ cost oil + cost remaining} \\
= \frac{1}{4}­\)

Is my approach correct? or did i get lucky? Bunuel gmatophobia someone tell­
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Re: During a certain month, 40 percent of all the oil used by a certain fa [#permalink] New post   10 May 2024, 09:14
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Manifesting710 wrote:
­let A = total oil

so oil used by oil heater = 0.4A
\(\\
\frac{Total cost of Oil used by oil heater}{0.4A} = \frac{1}{2}*\frac{total remaining oil cost}{ 0.6A}\\
\\
Cost Oil heater = \frac{1}{3}* Cost Remaining\\
\\
or 3*(C0st Oil Heater) = 1 * Cost Remaining\\
\\
\frac{Cost Oil}{Total Cost} = \frac{cost Oil }{ cost oil + cost remaining} \\
= \frac{1}{4}­\)

Is my approach correct? or did i get lucky? Bunuel gmatophobia someone tell­

­Your approach is logically sound.
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Re: During a certain month, 40 percent of all the oil used by a certain fa [#permalink] New post   10 May 2024, 09:32
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During a certain month, 40 percent of all the oil used by a certain factory was used by the oil heater. The cost per gallon of the oil used by the oil heater was half the cost per gallon of the rest of the oil used by the factory. For that month, the cost of the oil used by the oil heater was what fraction of the cost of all the oil used by the factory?

Let P be the cost per gallon for the rest of the factory.

Let T be the total number of gallons used.

So, the fraction we are looking for is the following:

\(\frac{{.40(T)(.5P)}}{{.40(T)(.5P) + .60(T)(P)}}\)

The Ts and Ps cancel out.

\(\frac{.2}{.2 + .60}\)

\(\frac{1}{4}\)

A. \(\frac{1}{6}\)

B. \(\frac{1}{5}\)

C. \(\frac{1}{4}\)

D. \(\frac{1}{3}\)

E. \(\frac{1}{2}\)­

Correct answer: C­
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Re: During a certain month, 40 percent of all the oil used by a certain fa [#permalink]
10 May 2024, 09:32
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