Answer

Verified

456.3k+ views

Hint: In this question first assume any variable for the number of winners and assume another variable for the rest of the candidates, then the sum of these variables are the total number of participants, use this concept to reach the solution of the question.

Let the number of winners be x.

And the rest of the candidates be y.

Now it is given that the total participants is 63.

$ \Rightarrow x + y = 63.................\left( 1 \right)$

Now according to the question winners get a prize of Rs. 100.

And the rest of the candidates get a prize of Rs. 25.

Total prize money is Rs. 3000

Now, convert this information into linear equation we have,

$ \Rightarrow 100x + 25y = 3000$

Now, divide by 25 in above equation we have,

$ \Rightarrow 4x + y = 120...............\left( 2 \right)$

From equation (1)

$y = 63 - x$

Substitute this value in equation (2) we have,

$

\Rightarrow 4x + 63 - x = 120 \\

\Rightarrow 3x = 120 - 63 = 57 \\

\Rightarrow x = \dfrac{{57}}{3} = 19 \\

$

So, the total number of winners in an essay competition is 19.

Note: Whenever we face such types of questions first assume the variables for winners and rest of the participants as above then convert the given information into linear equations as above then solve these two equation using substitution method as above or we can use elimination method by directly subtracting equation (1) from equation (2), we will get the required number of winners in an essay competition.

Let the number of winners be x.

And the rest of the candidates be y.

Now it is given that the total participants is 63.

$ \Rightarrow x + y = 63.................\left( 1 \right)$

Now according to the question winners get a prize of Rs. 100.

And the rest of the candidates get a prize of Rs. 25.

Total prize money is Rs. 3000

Now, convert this information into linear equation we have,

$ \Rightarrow 100x + 25y = 3000$

Now, divide by 25 in above equation we have,

$ \Rightarrow 4x + y = 120...............\left( 2 \right)$

From equation (1)

$y = 63 - x$

Substitute this value in equation (2) we have,

$

\Rightarrow 4x + 63 - x = 120 \\

\Rightarrow 3x = 120 - 63 = 57 \\

\Rightarrow x = \dfrac{{57}}{3} = 19 \\

$

So, the total number of winners in an essay competition is 19.

Note: Whenever we face such types of questions first assume the variables for winners and rest of the participants as above then convert the given information into linear equations as above then solve these two equation using substitution method as above or we can use elimination method by directly subtracting equation (1) from equation (2), we will get the required number of winners in an essay competition.

Recently Updated Pages

Which of the following is correct regarding the Indian class 10 social science CBSE

Who was the first sultan of delhi to issue regular class 10 social science CBSE

The Nagarjuna Sagar project was constructed on the class 10 social science CBSE

Which one of the following countries is the largest class 10 social science CBSE

What is Biosphere class 10 social science CBSE

Read the following statement and choose the best possible class 10 social science CBSE

Trending doubts

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Why is the Earth called a unique planet class 6 social science CBSE