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Percentage

by silverflamein » Fri Oct 21, 2011 1:58 pm
Acc to a survey conducted at a local law school, students like either cappuccino or tea (but not both). Male students who like cappuccino form 30% of all students. Female students who like tea form 25% of all students. Given that the ratio of male students to female students is 3:2. What percent of the female students like cappuccino ???

A) 70%

B) 62.5%

C) 55.75%

D) 40%

E) 37.5%
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by neelgandham » Fri Oct 21, 2011 4:49 pm
Method 1

Let the total no. of students be S

# of Male students who like cappuccino = MC = (30/100)*S
# of Male students who like Tea = MT = ?
# of Female students who like cappuccino = FC = ?
# of Female students who like Tea = FT = (25/100)*S

Total number of students = MC+MT+FC+FT = S

=> 0.3*S+MT+FC+0.25*S = S

=> MT+FC = 0.45 S - (1)

Total # of males/ Total # of females = 3/2

=> (MC+MT)/(FC+FT) = 3/2
=> (0.3*S+MT)/(FC+0.25*S) = 3/2 - (2)

Solving 1 and 2,
we get MT = 0.3*S and FC = 0.15*S

Question posed = (FC/(FC+FT))*100 ? = 0.15*S/((0.15*S)+(0.25*S)) =[spoiler] 37.5%[/spoiler] Option E

Method 2

Let the # of students be 100

MC = 30, Ratio of males to females = 3:2 = 6:4 = 60:40, so MT = 60-MC = 60-30 = 30
FT = 25 FC = 100 - MC - MT - FC = 15

(FC/(FT+FC))*100 = (15/40)*100 = 37.5[/u]
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