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Difficulty:
25%
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76% (01:32) correct
24%
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wrong
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Three friends were working on a college project. The amount of time that the three friends worked on the project were in the ratio 4: 5: 7. If the total number of hours taken to complete the task is an integer less than 50 and the time spend by each friend is also an integer, then which of the following could be the time taken by the friend who spent least time on the project?
A) 3
B) 8
C) 10
D) 11
E) 16
A) 3
B) 8
C) 10
D) 11
E) 16
13 Feb 2020, 00:14
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Raxit85
Three friends were working on a college project. The amount of time that the three friends worked on the project were in the ratio 4: 5: 7. If the total number of hours taken to complete the task is an integer less than 50 and the time spend by each friend is also an integer, then which of the following could be the time taken by the friend who spent least time on the project?
A) 3
B) 8
C) 10
D) 11
E) 16
A) 3
B) 8
C) 10
D) 11
E) 16
Solution 1:
- • Ratio of time taken by friends =\( 4: 5: 7.\)
- o Let \(4x, 5x\), and \(7x\) be the time taken by friends.
- o \(4x + 5x + 7x =16x < 50\)
- o \(4x, 5x\), and \(7x\), are integers.
- o We need to find the value of \(4x\).
o Since \(4x\) is an integer, time taken by him will be a multiple of \(4\).
o In the answer choices, only options B and E are multiple of \(4\).
• Option B: \(4x = 8, x = 2\)
- o \(16*x =16*2 =32\), which is less than \(50\), \(4x = 8\) is a possible answer.
- o \(16*4=64\), which is not less than \(50\), \(4x = 16\) is not possible.
Solution 2:
- • Ratio of time taken by friends =\( 4: 5: 7\).
- o Let \(4x, 5x\), and \(7x\) be the time taken by friends.
- o \(4x + 5x + 7x =16x < 50\)
o \(x < \frac{50}{16}\)
o \(x < 3.125\), \(x\) can \(1, 2\), and \(3\).
- o Possible values of \(4x\) are:
- o \(4*1=4\)
o \(4*2=8\)
o \(4*3=12\),
Hence, the correct answer is Option B.
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