Sheridan Service sells oil at a markup of $33 \%$ of the selling price. Sheridan paid $\$ 1.05$ per litre of oil.
(a) What is the selling price per litre?
(b) What is the rate of markup based on cost?
(a) The selling price per litre is $\$ \square$.
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
(b) The rate of markup based on cost is $\%$
(Round the final answer to two decimal places as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：Let x be the selling price per litre. Then, the markup is 0.33x.

Step 2 ：The cost price per litre is $1.05, so the selling price is the cost price plus the markup: x = 1.05 + 0.33x.

Step 3 ：Solve for x: 0.67x = 1.05.

Step 4 ：Divide both sides by 0.67: x = \(\frac{1.05}{0.67}\approx 1.5672\).

Step 5 ：Round the selling price to the nearest cent: \(\boxed{\$1.57}\) per litre.

Step 6 ：To find the rate of markup based on cost, divide the markup by the cost price: \(\frac{0.33x}{1.05}\).

Step 7 ：Substitute the selling price x = 1.5672: \(\frac{0.33(1.5672)}{1.05}\approx 0.4905\).

Step 8 ：Multiply by 100 to get the percentage: 0.4905 * 100 \approx 49.05\%.

Step 9 ：Round the rate of markup to two decimal places: \(\boxed{49.05\%}\).