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08 Jul 2019, 02:56
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B
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Difficulty:
15%
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Question Stats:
88% (01:28) correct
13%
(01:38)
wrong
based on 56
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The ratio of violinists to cellists at a conservatory is 3 to 1. If 180 of the violinists depart, and all the cellists remain, the result is a new ratio of 3 violinists to 2 cellists. How many cellists are enrolled at the conservatory?
A. 100
B. 120
C. 240
D. 300
E. 360
A. 100
B. 120
C. 240
D. 300
E. 360
08 Jul 2019, 03:08
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Bunuel
The ratio of violinists to cellists at a conservatory is 3 to 1. If 180 of the violinists depart, and all the cellists remain, the result is a new ratio of 3 violinists to 2 cellists. How many cellists are enrolled at the conservatory?
A. 100
B. 120
C. 240
D. 300
E. 360
A. 100
B. 120
C. 240
D. 300
E. 360
V:C = 3:1
—> Values of V & C respectively = 3k & k
180 V departs —> Remaining V = 3k - 180
New ratio = 3:2
—> (3k - 180)/k = 3/2
—> 6k - 360 = 3k
—> 3k = 360
—> k = 120
Cellists = k = 120
IMO Option B
Pls Hit kudos if you like the solution
Posted from my mobile device
08 Jul 2019, 06:39
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If 180 violinists were to leave, the ratio would be cut in half, from 3 to 1 to 3 to 2. So 180 must be half of the total number of violinists, and we have 360 violinists, and thus, using the 3 to 1 ratio, 120 cellists.
