Question

An exam of 145marks contains 50 questions. If
some of the questions are of two marks and
some are of five marks, then the number of two
questions is​

Answer 1

Answer:

Let the no. of two mark question be 'x'

and the no. of five mark question be 'y'

According to question :

x+y = 50 --------- (1) eqn.

2x + 5y = 145 ---------(2)eqn.

equation (1)×2 we get

2x +2y = 100 -------- (3) eqn.

Now, subtract eqn. (3) from eqn. (2) we get

2x + 5y = 145

2x + 2y = 100

-------------------------

3y = 45

=> y = 15

put this value of y in eqn. (1) we get

x = 35 ( which is no. of two mark question )

Answer 2

Given,

There are 2 marks questions and 5 marks questions.

Total marks = 145 marks

Total questions = 50

To find,

Total number of 2 marks questions.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the total number of 2 marks questions = x

And, let the total number of 5 marks questions = y

According to the data mentioned in the question,

(2×x) + (5×y) = 145

2x + 5y = 145 ....(1)

And,

x + y = 50

2x+2y = 100....(2)

By subtracting (1) from (2), we get that,

2x+5y-2x-2y = 145-100

3y = 45

y = 15

By putting the value of "y" into (2), we get that,

2x + (2×15) = 100

2x + 30 = 100

2x = 100-30

2x = 70

x = 35

Number 2 marks questions = 35

Hence, there are 35 questions of 2 marks.