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# A barrel crude oil is extracted from a shale at a cost of $51$ dollars, and then transported to and from the refinery at a cost of $6$ dollars for each direction. Oil is processed three times at the refinery plant, at a cost of $9$ dollars each time. What is the profit in dollars per barrel, if the barrel is sold for $93$ dollars. (Profit is equal to revenue minus expenses).A. $1$ B. $2$ C. $3$ D. $4$

Last updated date: 14th Sep 2024
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Hint: The profit is incurred in selling oil, when the cost of selling is more than the cost at which it is produced (which includes all the cost extraction, transportation, refining, etc.)

The crude oil is extracted from shale at a cost,
${C_E} = 51$ dollars.
Cost of transportation in single direction to the refinery is,
${C_t} = 6$ dollars.
Cost of transportation in two directions direction (to and from the refinery),
${C_T} = 2 \times 6 = 12$ dollars.
The cost of refining the crude oil single time is,
${C_r} = 9$ dollars.
But the oil is refined 3 times. So, the total cost of refining the oil is,
${C_R} = 3 \times 9 = 27$ dollars.
Total cost incurred in converting the crude oil into a processed or refined oil is the cost price value and is given by,
$\Rightarrow CP = {C_E} + {C_T} + {C_R} \cdots \left( 1 \right)$
Substituting the value of ${C_E},{C_T}$ and ${C_R}$ in equation (1), we get
$\Rightarrow CP = 51 + 12 + 27$
$\Rightarrow CP = 90$ dollars.
The cost price which is incurred in producing refined oil is $90$ dollars per barrel.
The selling price of one barrel of oil is,
$\Rightarrow SP = 93$ dollars.
Clearly we can say that selling price is more than cost price. Therefore profit is calculated as,
$\Rightarrow P = SP - CP \cdots \left( 2 \right)$
Substituting the value of $SP$ and $CP$ in equation (2),we get
$\Rightarrow P = 93 - 90 \\ \Rightarrow P = 3 \\$
Therefore, the profit in dollars by selling one barrel of refined oil is $3$ .

So, the correct answer is “Option C”.

Note: The most important thing in this question is to analyze all the costs which have to be included in the refining of oil from the time of its extraction to the time at which it is sold. The cost like cost of extraction, cost of transportation, cost of refining, etc., comes under the category of cost price Also the number times each process takes place should be carefully examined and multiplied with that cost