Question

hi good morning solve this problem ​

Answer 1

Given:

Total no. of participants= 63

Total prize money, M= ₹3000

Fixed prize money for winners,W= ₹100

Fixed prize money for participants who doesn't win, P= ₹25

To Find:

Total no. of winners

Solution:

Let the total no. of winners be x

Then the participants who doesn't win will be 63-x

Let the total amount of prize money distributed to winners be A and the total amount of prize money distributed to rest participants be B

So,

$\longrightarrow\rm{A=W\times No.\ of\ Winners}$

$\longrightarrow\rm{A=100\times x}$

$\longrightarrow\rm{A=100x}$

Also,

$\longrightarrow\rm{B=P\times No.\ of\ remaining\ participants}$

$\longrightarrow\rm{B=25\times(63-x)}$

$\longrightarrow\rm{B=1575-25x}$

$\rule{190}{1}$

Now, according to question

$\longrightarrow\rm{M=A+B}$

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

$\longrightarrow\rm{3000-1575=100x-25x}$

$\longrightarrow\rm{1425=75x}$

$\longrightarrow\rm{75x=1425}$

$\longrightarrow\rm{x=\dfrac{\cancel{1425}}{\cancel{75}}}$

$\longrightarrow\rm\green{x=19}$

Hence, the total no. of winners are 19.

Answer 2

$\large\underline\bold{Question:-}$

The organizers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3000. Find the number of winners, if the total number of participants is 63.

$\large\underline\bold{Answer:-}$

$\small\underline\bold{Given:-}$

$\sf\ Total\:no\:of\: participants$

$\sf\ Total\:prize\:money= 3000$

$\sf\ Fixed\:prize\: money\:for\:winners=100$

$\sf\ Fixed\:prize\:money\:for\: winners\:who\: doesn't\:win=25$

$\small\underline\bold{To\:Find:-}$

$\sf\ Total\:no\:of\: participants$

$\small\underline\bold{Required\: Solution:-}$

$\sf\ Let\:the\:no\:of\: winners\:be\:x.$

$\sf\ And\:the\:no\:of\: runner\:ups\:be\:63-x$

⟹$\sf\ 100(x+25(63-x)=3000$

⟹$\sf\ 100x+1575-25x=3000$

⟹$\sf\ 75x+1575=3000$

⟹$\sf\ 75x=3000-1575$

⟹$\sf\ 75x=1425$

⟹$\sf\large x= \frac{1425}{75}$

✝️$\large\underline\bold\purple{x=19}$