Unit operating expenses for an item costing $$25$ are estimated at $40\%$ of cost$,$ and the desired operating profit is $10\%$ of cost$.$

a$.$ Determine the selling price. $($Do not round intermediate calculations and round your final answer to $2$ decimal places.$)$

Selling price

$ $$

b$.$ Determine the rate of markup on cost$.($Do not round intermediate calculations and round your final answer to $1$ decimal place

Markup on cost $\%$

c$.$ Determine the rate of markup on selling price. $($Do not round intermediate calculations and round your final answer to $1$ decim place.$)$

Markup on selling price $$