
Yash scored marks in a test, getting marks for each right answer and losing mark for each wrong answer. Had marks been awarded for each correct answer and marks been deducted for each incorrect answer, then Yash would have scored marks. How many questions were there in the test?
Answer
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Hint: The question is related to the linear equation in two variables. Try to make two equations using the information given in the problem statement and solve them simultaneously.
In the question, it is given that Yash scored marks in a test, getting marks for each right answer and losing mark for each wrong answer. So, we will consider as the total number of questions that were answered correctly by Yash and as the total number of answers that were answered incorrectly.
Now, in the first case, it is given that for each correct answer marks are awarded. So, for correct answers, total marks awarded are equal to . Also, for each wrong answer, mark is deducted. So, for wrong answers, total marks deducted is equal to . So, the total marks obtained will be . But it is given that the total marks obtained are . So.
Now, in the second case, it is given that for each correct answer marks are awarded. So, for correct answers, total marks awarded are equal to . Also, for each wrong answer, mark is deducted. So, for wrong answers, total marks deducted is equal to . So, the total marks obtained will be . But it is given that the total marks obtained are . So.
Now, we will solve the linear equations to find the values of and .
From equation , we have
On substituting in equation , we get
Now, on substituting in the equation , we get
So, the total number of questions in the test is equal to .
Note: While solving the equations, make sure that the substitutions are done correctly and no sign mistakes are present. Sign mistakes can cause the final answer to be wrong.
In the question, it is given that Yash scored
Now, in the first case, it is given that for each correct answer
Now, in the second case, it is given that for each correct answer
Now, we will solve the linear equations to find the values of
From equation
On substituting
Now, on substituting
So, the total number of questions in the test is equal to
Note: While solving the equations, make sure that the substitutions are done correctly and no sign mistakes are present. Sign mistakes can cause the final answer to be wrong.
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