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In a beauty competition, 2/5 of the participants were eliminated in the first round. 2/3 of the remaining participants qualified from the second to the third round and half of the participants of the third round got into the final round. In the final round, 2/3 of the remaining participants lost the competition, while two of them won the competition. How many participants were there in the competition?

In a beauty competition, 2/5 of the participants were eliminated in the first round. 2/3 of the remaining participants qualified from the second to the third round and half of the participants of the third round got into the final round. In the final round, 2/3 of the remaining participants lost the competition, while two of them won the competition. How many participants were there in the competition? Correct Answer 30

Let the number of participants be ‘x’

No. of participants eliminated in first round = (2/5)x

No. of participants in the second round = x – (2/5)x = (3/5)x

No. of participants qualified to third round = (2/3) × (3/5)x = (2/5)x

No. of participants qualified to final round = (1/2) × (2/5)x = (1/5)x

No. of participants that won in final round = (1/5)x – (2/3) × (1/5)x = (1/5)x – (2/15)x = x/15

But, only two participants won the competition,

⇒ x/15 = 2

⇒ x = 30

∴There were 30 participants in the competition

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