Question

A question paper consists of questions, each carrying $ \dfrac{1}{2} $ mark, $ 1 $ mark and $ 2 $ marks in the ratio $ 2:2:1 $ . If the maximum marks in the exam is $ 100 $ , then find the number of questions of 2 marks.
(a) $ 40 $
(b) $ 20 $
(c) $ 60 $
(d) $ 30 $

Answer 1

Hint: As we know that the above given question is a word problem. A problem is a mathematical question written as one sentence or more describing a real life scenario where that problem needs to be solved by the way of mathematical calculation. We can solve the given problem by applying the method of mathematical numbers and form the equation according to the question.

Complete step-by-step answer:
We need to first understand the requirement of the question which is the number of questions of $ 2 $ marks. Let us assume the number of questions each carrying
$ \dfrac{1}{2} $ mark, $ 1 $ mark and $ 2 $ marks be $ 2x,2x $ and $ x $ respectively.
According to the question, the total mark is $ 100 $ . So we can say that
 $ 2x + 20 + x = 100 $ ,
On further solving we have
 $ 5x = 100 \\
\Rightarrow x = 20 $ .
Now substituting the value $ x $ in their numbers,
Number of questions carrying
 $ \dfrac{1}{2} $ mark is $ 2x $ i.e. $ 2 \times 20 = 40 $ .
Similarly the number of questions carrying $ 1 $ mark is $ 2x $ . So it gives $ 2 \times 20 = 40 $ . And the number of questions carrying $ 2 $ marks is $ x $ i.e. $ 20 $ .
Hence the correct option is (b) 20.
So, the correct answer is “Option B”.

Note: We should always be careful what the question is asking. Based on the requirement and by observing all the necessary information that is already available in the question we gather the information and then create an equation or by unitary method whichever is applicable, then we solve the problem and then verify the answer by putting the value in the problem and see whether we get the same answer or not.