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28 Jul 2026, 02:27
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
55% (02:39) correct
45%
(03:02)
wrong
based on 38
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For any given month, Mateus pays taxes on his monthly earnings: 15% of the first €2,000 of his earnings plus the lesser of 500€ and 40% of the portion of his earnings above €2,000. Mateus paid more tax on his earnings in February than in January, but in both months, he paid taxes equal to 20% of his earnings. By what fraction were his earnings in February higher than his earnings in January?
(A) \(\frac{2}{5}\)
(B) \(\frac{1}{2}\)
(C) \(\frac{3}{5}\)
(D) \(\frac{2}{3}\)
(E) \(\frac{5}{8}\)
(A) \(\frac{2}{5}\)
(B) \(\frac{1}{2}\)
(C) \(\frac{3}{5}\)
(D) \(\frac{2}{3}\)
(E) \(\frac{5}{8}\)
29 Jul 2026, 12:28
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kevincan
Since the Feb and Jan tax are \(20\%\) of his earnings, we know that his earnings on both the month are more than \(2000\).
\(15\%\) tax on \(2000 = 300\)
Also if the portion above \(2000\) is \(1250\) then \(40\%\) tax comes out to be \(500\).
\((a)\) If his extra portion is greater than or equal to \(1250\) then he will pay \(500.\)
\((b)\) If his extra portion is less than \(1250\) he will pay \(40\%\) of that.
Using case \((a)\) to find his total salary, \(x\).
\(300 +500 = .20 (x) \)
\(x= 4000\)
Using case (b) to find his total salary :
\(y=\) portion above \(2000\)
\(300 + .40 (y) = .20 (2000 +y)\)
\(y= 500\)
Total salary using case (b)-> \(2000 +500 = 2500\)
Hence Mateus Feb's earning must be \(4000\) and Jan's earning must be \(2500\)
Feb's extra income \(4000 -2500 = 1500\)
Required fraction \(\frac{1500}{2500}= \frac{3}{5}\)
Ans C
Hope it helped.
02 Aug 2026, 22:39
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