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26 Apr 2026, 13:39
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Michael bought 12 concert tickets, each at the same price. Later, he resold all 12 tickets for the same higher price per ticket and paid t percent tax on the profit from the resale. After paying the tax, what was Michael’s net profit from the resale?
(1) The resale price per ticket was 40 dollars more than the purchase price per ticket.
(2) If the tax rate had been 15 percentage points higher, then Michael’s net profit would have been 360 dollars.
(1) The resale price per ticket was 40 dollars more than the purchase price per ticket.
(2) If the tax rate had been 15 percentage points higher, then Michael’s net profit would have been 360 dollars.
26 Apr 2026, 13:39
Kudos
Bookmarks
Official Solution:
Michael bought 12 concert tickets, each at the same price. Later, he resold all 12 tickets for the same higher price per ticket and paid \(t\) percent tax on the profit from the resale. After paying the tax, what was Michael’s net profit from the resale?
Let purchase price per ticket be \(p\) and resale price per ticket be \(r\).
Pre tax profit = \(12 * (r - p)\)
Net profit after tax = \(12 * (r - p) * (1 - \frac{t}{100})\)
(1) The resale price per ticket was 40 dollars more than the purchase price per ticket.
This gives:
\(r - p = 40\), so pre tax profit = \(12 * 40 = 480\).
But \(t\) is unknown, so net profit after tax is not fixed.
Not sufficient.
(2) If the tax rate had been 15 percentage points higher, then Michael’s net profit would have been 360 dollars.
Let pre tax profit be \(P\). If the tax rate were \(t + 15\), then net profit would be:
\(P * (1 - \frac{t + 15}{100}) = 360\)
This is 1 equation with 2 unknowns, \(P\) and \(t\), so net profit after the original tax is not fixed.
Not sufficient.
(1)+(2) From (1), \(P = 480\). Substitute into (2):
\(480 * (1 - \frac{t + 15}{100}) = 360\)
\(t = 10\)
So the actual net profit is:
\(480 * (1 - \frac{10}{100}) = 480 * 0.9 = 432\).
Sufficient.
Answer: C
Michael bought 12 concert tickets, each at the same price. Later, he resold all 12 tickets for the same higher price per ticket and paid \(t\) percent tax on the profit from the resale. After paying the tax, what was Michael’s net profit from the resale?
Let purchase price per ticket be \(p\) and resale price per ticket be \(r\).
Pre tax profit = \(12 * (r - p)\)
Net profit after tax = \(12 * (r - p) * (1 - \frac{t}{100})\)
(1) The resale price per ticket was 40 dollars more than the purchase price per ticket.
This gives:
\(r - p = 40\), so pre tax profit = \(12 * 40 = 480\).
But \(t\) is unknown, so net profit after tax is not fixed.
Not sufficient.
(2) If the tax rate had been 15 percentage points higher, then Michael’s net profit would have been 360 dollars.
Let pre tax profit be \(P\). If the tax rate were \(t + 15\), then net profit would be:
\(P * (1 - \frac{t + 15}{100}) = 360\)
This is 1 equation with 2 unknowns, \(P\) and \(t\), so net profit after the original tax is not fixed.
Not sufficient.
(1)+(2) From (1), \(P = 480\). Substitute into (2):
\(480 * (1 - \frac{t + 15}{100}) = 360\)
\(t = 10\)
So the actual net profit is:
\(480 * (1 - \frac{10}{100}) = 480 * 0.9 = 432\).
Sufficient.
Answer: C
