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Let the original sales amount be x. Then the profit you make would be .45x. If I reduce the profit margin to 40% and increase sales by 10%, this becomes equal to .40*1.1*x = .44x. Taking the ratio, we get 44/45.
Profit on sale is defined as the percentage profit w.r.t sale price, whereas profit on cost is defined w.r.t. the cost price. So, profit on sale = (S.P-C.P)/S.P * 100 whereas profit on cost is (S.P.-C.P)/C.P*100. If nothing is mentioned, then profit is always taken w.r.t cost.
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