Question

Q: The organisers of an essay competition decide that a winner in the competition gets a prize of Rupees 100 & a participant who does not win get a prize of Rupees 25. The total prize money distributed is Rupees 3000 . Find the number of winners if the total number of participants is 63 .
Solve :

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Answer 1

$\sf\underline{Question:}$ The organisers of an essay competition decide that a winner in the competition gets a prize of Rupees 100 & a participant who does not win get a prize of Rupees 25. The total prize money distributed is Rupees 3000 . Find the number of winners if the total number of participants is 63.

$\sf\underline{Have \: to \: find}$ $\downarrow$

❍ $\sf{Number \: of \: Winners}$

$\sf\underline{Solution}$ $\downarrow$

$\sf{Let \: the \: winners \: be = x}$

$\sf{Let \: the \: losers \: be = 63-x}$

|| Number of prize to the winners: X × 100 = 100x ||

|| Number of prize to losers : (63-x)25

• $\sf{63 × 25 - 25x}$
• $\sf{1575 - 25x}$

$\sf{100x + 1575 - 25x = 3000}$

$\sf{= 75x = 3000 - 1575}$

$\sf{= 75x = 1425}$

$\sf{x}$ $\rightarrow$ $\dfrac{1425}{75}$ = $\dfrac{285}{15}$ = $\dfrac{57}{3}$ = $\sf{19.}$

★ The number of winners is: $\sf\underline\red{19}$.