In a particular college, the number of students is increased by 20%. Due to a new ordinance passed by the government, education for the girls was made free. To collect the fee, which was numerically equal to what was collected last year, the college had to charge 25% more from the boys compared to last year. Find the ratio of boys to girls this year.
(a) 2:1
(b) 1:2
(c) 4:3
(d) 3:4
Answers
Given : In a particular college, the number of students is increased by 20%. Due to a new ordinance passed by the government, education for the girls was made free. To collect the fee, which was numerically equal to what was collected last year, the college had to charge 25% more from the boys compared to last year
To find : ratio of boys to girls
Solution:
Let say Last Year students were = S
& Fee was F
Fees collected = SF
the number of students is increased by 20%.
=> This years Students = S + (20/100)S = 1.2S
Fees increased by 25 %
This year Fee = F + (25/100)F = 1.25F
Fee collected = As collected last year = SF
Number of Boys = SF/ 1.25F = 0.8S
Boys = 0.8S
Students = 1.2S
Girls = 1.2S - 0.8S = 0.4S
Boys : Girls = 0.8S : 0.4S
=> Boys : Girls = 2 :1
ratio of boys to girls this year. is 2:1
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