Ex 2.2, 16 The organisers of an essay competition decide that a winner in the competition gets a prize of Rs 100 & a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3,000. Find the number of winners, if the total number of participants is 63.Given,
Prize given to the Winner = Rs 100
Prize given to the participants who did not win = Rs 25
Total Prize money = Rs 3,000
Total number of participants = 63
Let the numbers of winners = 𝑥
Then,
Total no. of participants = Number of winners + Number of participants who did not win
63 = 𝑥 + Number of participants who did not win
63 − 𝑥 = Number of participants who did not win
Number of participants who did not win = 63 − 𝑥
Total amount given to the winners
= Number of winners × Amount given to 1 winner
= 𝑥 × 100
= 100𝑥
Total amount given to the participants who did not win
= Number of participants who did not win × Amount given to 1 participant
= (63 − 𝑥) × 25
= 63 × 25 − 𝑥 × 25
= 1575 − 25𝑥
Total prize money = Total amount given to winners + Total amount given to participants who did not win
3000 = 100𝑥 + 1575 − 25𝑥
100𝑥 + 1575 − 25𝑥 = 3000
75𝑥 + 1575 = 3000
75𝑥 = 3000 − 1575
75𝑥 = 1425
𝑥 = 1425/75
𝑥 = 19
Therefore, the number of winners = 19

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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