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08 Mar 2024, 02:30
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C
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Difficulty:
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Question Stats:
86% (01:22) correct
14%
(01:36)
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The ratio of apples, bananas, cantaloupes, and oranges at a fruit stand is 5:3:2:6, respectively. The total number of these fruits is 64. If 4 cantaloupes are added to the fruit stand, what is the new ratio of bananas to cantaloupes?
A. 1 : 2
B. 2 : 3
C. 1 : 1
D. 3 : 2
E. 2 : 1
A. 1 : 2
B. 2 : 3
C. 1 : 1
D. 3 : 2
E. 2 : 1
IMO C
If the total number of fruits is 64 and the ratio of apples, bananas, cantaloupes, and oranges is 5:3:2:6, then we can express this as fractions of the total:
Apples: \( \frac{5}{5+3+2+6} \times 64 = \frac{5}{16} \times 64 = 20 \)
Bananas: \(\frac{3}{5+3+2+6} \times 64 = \frac{3}{16} \times 64 = 12 \)
Cantaloupes:\( \frac{2}{5+3+2+6} \times 64 = \frac{2}{16} \times 64 = 8 \)
Oranges: \(\frac{6}{5+3+2+6} \times 64 = \frac{6}{16} \times 64 = 24 \)
Now, if 4 cantaloupes are added, the new number of cantaloupes becomes 8 + 4 = 12 .
The new ratio of bananas to cantaloupes becomes:
\(\frac{Bananas}{Cantaloupes} = \frac{12}{12} = 1:1 \)
Therefore, the answer is C
If the total number of fruits is 64 and the ratio of apples, bananas, cantaloupes, and oranges is 5:3:2:6, then we can express this as fractions of the total:
Apples: \( \frac{5}{5+3+2+6} \times 64 = \frac{5}{16} \times 64 = 20 \)
Bananas: \(\frac{3}{5+3+2+6} \times 64 = \frac{3}{16} \times 64 = 12 \)
Cantaloupes:\( \frac{2}{5+3+2+6} \times 64 = \frac{2}{16} \times 64 = 8 \)
Oranges: \(\frac{6}{5+3+2+6} \times 64 = \frac{6}{16} \times 64 = 24 \)
Now, if 4 cantaloupes are added, the new number of cantaloupes becomes 8 + 4 = 12 .
The new ratio of bananas to cantaloupes becomes:
\(\frac{Bananas}{Cantaloupes} = \frac{12}{12} = 1:1 \)
Therefore, the answer is C
08 Mar 2024, 02:59
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The original ratio is 5:3:2:6 (for 16 total fruits). Then for 64 fruits will be every fruit x4= 20:12:8:24.
At this point the ratio is 12:8 --> 3:2.
If 4 cantaloupes are added, the total cantaloupes will now be 12. Bananas are already 12. Hence 12:12 is the new ratio.
ANS C (1:1)
At this point the ratio is 12:8 --> 3:2.
If 4 cantaloupes are added, the total cantaloupes will now be 12. Bananas are already 12. Hence 12:12 is the new ratio.
ANS C (1:1)
