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Bunuel
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For administrative purposes, a local university divides its activities 09 Jul 2020, 03:59
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5% (low)

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95% (01:39) correct 5% (03:16) wrong based on 42 sessions

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For administrative purposes, a local university divides its activities among five separate colleges. According to the university charter, the College of Arts and Sciences is entitled to 80% of the university's office workers, while the remaining four colleges (Agriculture, Engineering, Health Science and Business) must divide the remaining office workers equally. If the College of Arts and Sciences merges with the College of Health Science, they will have 340 total office workers. How many office workers did the university originally employ?

A. 400
B. 420
C. 450
D. 500
E. 680
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A
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For administrative purposes, a local university divides its activities 09 Jul 2020, 04:04
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Bunuel
For administrative purposes, a local university divides its activities among five separate colleges. According to the university charter, the College of Arts and Sciences is entitled to 80% of the university's office workers, while the remaining four colleges (Agriculture, Engineering, Health Science and Business) must divide the remaining office workers equally. If the College of Arts and Sciences merges with the College of Health Science, they will have 340 total office workers. How many office workers did the university originally employ?

A. 400
B. 420
C. 450
D. 500
E. 680
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Let the total workers be W

Original number of workers in CAS = 0.8W
Original number of workers in CHS = 0.05W

After merger of CAS and CHS, final number of workers - 0.85W

As per the question stem, 0.85W = 340
=> W=400

OA : A
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For administrative purposes, a local university divides its activities 09 Jul 2020, 04:10
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Explanation:
the College of Arts and Sciences workers = 80%
Left 20% which is divided equally in Agriculture, Engineering, Health Science and Business i.e. 5% in each.
So ,the College of Arts and Sciences workers + Health Science =340
85% = 340
so 100% = 340/0.85 = 400

IMO-A
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For administrative purposes, a local university divides its activities 09 Jul 2020, 06:24
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Bunuel
For administrative purposes, a local university divides its activities among five separate colleges. According to the university charter, the College of Arts and Sciences is entitled to 80% of the university's office workers, while the remaining four colleges (Agriculture, Engineering, Health Science and Business) must divide the remaining office workers equally. If the College of Arts and Sciences merges with the College of Health Science, they will have 340 total office workers. How many office workers did the university originally employ?

A. 400
B. 420
C. 450
D. 500
E. 680
Show more

Let total office workers be \(X\),

Thus, workers of Arts and Sciences are \(0.8X\)

Therefore, workers of Agriculture, Engineering, Health Science and Business are \(0.2X\)

And workers of Agriculture, Engineering, Health Science and Business are equally divided.

Thus, workers of Health Science are \(\frac{0.2X}{4}\) = \(0.05X\)

Total workers of Health Science and Arts and Sciences are = \(0.05X\) + \(0.8X\) = \(0.85X\)

Given, \(0.85X\) = \(340\)

=>\( X\) = \(\frac{340}{0.85}\) = \(400\)

Total workers university originally employ are = \(400\)

IMO ans is A.
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