CVP Analysis

Good Day Sir
I came across this question and wanted to ask:

Dalton Co produces and sells a product for $90. The production for the
upcoming year is budgeted to be 30,000 units and Dalton Co expects all
the produced units to be sold.
The cost accountant has determined the break-even point (in revenue) to
be $600,000, whereas contribution to sales ratio is 40%.
What is the expected profit for the year?
A $840,000
B $960,000
C $720,000
D $980,000

I got the correct answer which is A.
As from their solution the correct way to get the answer was as follows:
The candidates need a thorough knowledge of break-even formulas
to solve this question.
Break-even revenue = Fixed costs / Contribution to sales ratio
Re-arranging the formula;
Fixed costs = Break-even revenue x Contribution to sales ratio
Fixed costs = $600,000 x 40%
Fixed costs = $240,000
Contribution per unit = Selling price x Contribution to sales ratio
Contribution per unit = $90 x 40%
Contribution per unit = $36
Total contribution = Units sold x Contribution per unit
Total contribution = 30,000 x $36
Total contribution = $1,080,000
Total profit = Total contribution – Fixed costs
Total profit = $1,080,000 – $240,000
Total profit = $840,000

However, for a section A question, this would take me a tremendous amount of time which I do not have.
I got my answer as follows:
Breakeven point (revenue) 600 000/90= 6667 units to break even.
Therefore 30000-6667= 23333units make a profit.
So to get the profit it is 90*40%
36*23333 units = 839988 (round up to 840 000).

My question is that is this a method I can use or did this answer just happen to be correct by chance?