During a certain month, 40% of all the oil used by a certain factory

Question

During a certain month, 40% of all the oil used by a certain factory was used by oil heaters. 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. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2

A. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2

gmatophobia · Answer

Assume that 100 gallons of oil was used.

40% of all the oil used by a certain factory was used by oil heaters.

The amount of oil used by oil heaters = 40% of 100 = 40 gallon
The amount of oil used by the factory = 60 gallon

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 -

The price of oil that was used by oil heaters = $1 / gallon
Therefore, the price of oil that was used by rest of the factory = $2 / gallon

For that month, the cost of the oil used by the oil heater = 40 * 1 = $40
For that month, the cost of the oil used by the rest of the factory = 60 * 2 = $120

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

Option C

Raman109 · Answer

Defining Variables :

Total oil used by the factory = O gallons. 
 Cost per gallon for oil not used by oil heaters = C dollars.   
  Calculating Amounts of Oil :

Oil used by oil heaters = 40% of O = 0.4O gallons. 
 Oil not used by oil heaters = 60% of O = 0.6O gallons.   
  Cost per Gallon for Oil Used by Heaters :

It's half the cost of the other oil, so C/2 dollars per gallon.   
  Calculating the Costs :

Cost for oil used by heaters = 0.4O gallons × C/2 dollars/gallon = 0.4O×C/2. 
 Cost for oil not used by heaters = 0.6O gallons × C dollars/gallon = 0.6O×C.   
  Total Cost :

Total cost = Cost for heaters + Cost for others. 
 =0.4O×C/2+0.6O×C. 
 =0.2O×C+0.6O×C  
 =0.8O×C.   
  Fraction of Total Cost for Heaters :

Fraction = Cost for heaters / Total cost. 
 =(0.2O×C)/(0.8O×C). 
 = 1/4 or 25%.

Purnank · Answer

take total oil as 100x and rate for y per gallon.
40% used by oil heater but amount is half of that for rest of the factory usage means y is for rest of the usage y/2 is for oil heater.
Total cost for oil heater = 40x*y/2 = 20xy
Cost for rest = 60x*y = 60xy
Fraction of cost for oil heater = 20xy / 80xy = 1/4
  Answer is C.

Armaan209 · Answer

This questions can be attempted in 2 ways ( Varibales or choosing values)

In this type of question both of the approaches will take the similar time.

The level mentiones in the tag should be 505 level

KarishmaB · Answer

Amount of oil used for heater : other is 40:60 = 2:3
Cost of oil used for heater : other is 1:2
On the ratio scale, the total cost of oil used for heater : other is 2*1 : 3*2 = 2:6 = 1:3

Hence 1/4th of the total cost is cost of oil used for heater.

Answer (C)

Ratio scale is discussed here:  https://youtu.be/5ODENGG5dvc

bumpbot · Answer

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During a certain month, 40% of all the oil used by a certain factory

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During a certain month, 40% of all the oil used by a certain factory