Solution to Contest #13

This numbers English contest has lots of numbers English to translate into calculation. It also requires some logic to set up the calculation.

The question seems quite tricky:

What is the expected loss in profit from March to April?

Some of you may be asking: "How can we have a loss in profits?" After all, losses and profits are opposites of each other; we should only have one or the other, right?

To explain this, let's consider a company that has a profit of $2,000 in Month 1 and a profit of $1,500 in Month 2. There is a $500 loss in profits from Month 1 to Month 2. Now do you understand how words are used in this way?

We need to start with the end of March production figures to build our figures for March and April.

At the end of March, an oil well was producing 50.5 m3 of oil per day and 72.1 m3 of water per day. Each month, the well's oil production decreases by 1.855% and water production increases by 2.011%.

To get the figures for the end of April, we simply make these calculations:

Oil rate = 50.5 m3 x (1 - 0.01855) = 49.56 m3 per day.

Water rate = 72.1 m3 x (1 + 0.02011) = 73.55 m3 per day.

Average oil rate = (50.5 + 49.56) /2 = 50.03 m3 per day

Average water rate = (72.1 + 73.55) / 2 = 72.82 m3 per day

Total oil production = 50.03 m3 / day x 30 days = 1,500.9 m3
Total water production = 72.82 m3 / day x 30 days = 2,184.6 m3

The figures for March are going to be more difficult to calculate because the 50.5 and 72.1 are at the end of the month. In English, it is important to base the % calculation on the starting figures, which, in this case, are for the beginning of March, which is what we are trying to solve. So the calculations work like this:

Oil rate = 50.5 / (1 - 0.01855) = 51.45 m3 per day.
Water Rate = 72.1 / (1 + 0.0211) = 70.61 m3 per day.

Average oil rate = (51.45 + 50.5) / 2 = 50.98 m3 per day.
Average water rate = (70.61 + 72.1) / 2 = 71.36 m3 per day.

Monthly oil production = 50.98 x 31 days = 1580.4 m3.
Monthly water production = 71.36 x 31 days = 2,212.2 m3.

The next step is calculating the profits for March and April:

It costs $140,250 to operate this well each month.
[It also costs] $51.90 to process one cubic meter of oil and $15.50 to dispose one m3 of water.

For March the costs are: 140,250 + 51.90 x 1580.4 + 15.50 x 2212.2 = $256,563.
For April the costs are: 140,250 + 51.90 x 1500.9 + 15.50 x 2184.6 = $252,008.

Oil price is expected to be $575.00 per m3.

Supposedly, the petroleum company already knew the price of oil in March, but this figure was not provided. The "expected" price is for April. Because this information is somewhat vague, we can only use the best information we have. We will assume that the oil price for both months is $575.00 per m3.

March revenues = 1580.4 x 575.00 = $908,730
April revenues = 1500.9 x 575.00 = $863,018.

What is the expected loss in profit from March to April?

March profit = $908,730 - $256,563 = $652,157
April profit = $863,018 - $252,008 = $611,010

So the loss in profits (from March to April) is $652,157 - $611,010 = $41.147

If you were watching your calculations closely, much of this loss in profits can be attributed to March having one extra day.