A group of 25 children went to the circus, 60% of whom liked the clown

Solution:

Total children = 25

• Children who liked clown =\(\frac{ 60}{100}*25\) = 15

o Boys who liked clowns = b + 3
o Girls who liked the clown = 12 - b
• Children who didn’t liked the clown = 25-15 = 10

o Boys who didn’t liked clown = b
o Girls who didn’t liked clown = 10 - b

Total number of boys is one more than total number of girls

• b+b +3 = 12 – b + 10 - b + 1
• 2b+3 = -2b+23
• 4b = 20
• b = 5

The number of girls who didn’t liked the clown = 10 – 5 = 5
Hence, the answer is A.

Question:
A group of 25 children went to the circus, 60% of whom liked the clowns. If the number of boys who liked the clowns was three more than the number who didn't, and the number of boys was one larger than the number of girls, then how many girls did not like the clowns?

Solution:
Number of children who liked the clowns = 60% of 25 = 15
# children who didn't like the clowns = 10

Difference between boys and girls (boys being greater) = 1
Total of boys and girls = 25
So, number of boys = (25+1)/2 = 13

Difference between boys who liked and disliked clowns (boys who liked clowns are greater) = 3

Total boys who liked and disliked clowns = 13

Thus, number of boys who liked clowns
= (13+3)/2 = 8
=> Number of boys who disliked clowns
= 13-8 = 5
[or you can simply do: (13-3)/2 = 5]

Total children who disliked clowns = 10

=> Girls who disliked clowns
= 10-5 = 5

Answer A

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-------------Boys-----------Girls------------Total

Like---------8---------------7----------------15

Don't Like--5---------------5----------------10

Total--------13------------12---------------25

Girls who do not like clowns = 5(A)

Since the number of boys was one more than the number of girls, there were 13 boys and 12 girls. Furthermore, since the number of boys who liked the clowns was three more than the number who didn't, 8 boys liked clowns, and 5 didn’t. Finally, since 60% of the 25 children liked the clowns, 0.6 x 25 = 15 children liked clowns, and 10 didn’t. Since 5 of the 10 children who didn’t like clowns were boys, the other 5 children must be girls.

Answer: A

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