Read the given information carefully and answer the following questions.
Following paragraph shows the information about four students (A,B, C and D) who have attempted
English exams. There are two types of questions i.e. Shorts questions and Long questions.

Short questions section:

I. Each question is of 5 marks.

II. Candidates have to attempt at least 6 out of every 7 questions.

Long questions section:

I. Each question is of 10 marks.

II. Candidates have to attempt at least 7 out of every 9 questions

Note: 0.5 marks will be deducted for each spelling error and 0.75 marks will be deducted if he forgot to
write a whole word.
In this exam, there are total 42 short and 18 long questions. B corrects 14 long questions and obtained
131 marks whereas he obtained 175 marks in short section. Total marks obtained by A in short questions
is 160 by attempting 38 questions. C attempted all the short questions and corrects as twice as number of
questions correct in long section and got 150.5 marks in the long questions. D answered correctly 15 long
questions and ratio of spelling errors in long to short section is 3:4.

If A made 25% more spelling mistakes in the long section than in the short section, answered 16 long questions correctly, and scored 135 marks in the long section, then how many questions did A answer incorrectly in the short section?

Question

Read the given information carefully and answer the following questions.
Following paragraph shows the information about four students (A,B, C and D) who have attempted
English exams. There are two types of questions i.e. Shorts questions and Long questions.

Short questions section:

I. Each question is of 5 marks.

II. Candidates have to attempt at least 6 out of every 7 questions.

Long questions section:

I. Each question is of 10 marks.

II. Candidates have to attempt at least 7 out of every 9 questions

Note: 0.5 marks will be deducted for each spelling error and 0.75 marks will be deducted if he forgot to
write a whole word.
In this exam, there are total 42 short and 18 long questions. B corrects 14 long questions and obtained
131 marks whereas he obtained 175 marks in short section. Total marks obtained by A in short questions
is 160 by attempting 38 questions. C attempted all the short questions and corrects as twice as number of
questions correct in long section and got 150.5 marks in the long questions. D answered correctly 15 long
questions and ratio of spelling errors in long to short section is 3:4.

If A made 25% more spelling mistakes in the long section than in the short section, answered 16 long questions correctly, and scored 135 marks in the long section, then how many questions did A answer incorrectly in the short section?

Accepted Answer

**Solution:**

1. Let the number of spelling errors A made in the short section be $4x$.

2. Since A made 25% more spelling mistakes in the long section than in the short section, spelling errors in long section = $4x + 0.25 	imes 4x = 5x$.

3. A answered 16 long questions correctly, each worth 10 marks, and scored 135 marks in the long section after deductions:
   $$16 	imes 10 - 5x 	imes 0.5 = 135$$
   $$160 - 2.5x = 135$$
   $$2.5x = 25$$
   $$x = 10$$

4. Therefore, spelling errors in short section = $4x = 40$.

5. Let the number of correctly answered short questions by A be $a$.

6. A scored 160 marks in the short section after deductions:
   $$a 	imes 5 - 40 	imes 0.5 = 160$$
   $$5a - 20 = 160$$
   $$5a = 180$$
   $$a = 36$$

7. A attempted 38 short questions in total.

8. Number of incorrectly answered short questions = Total attempted - Correctly answered = $38 - 36 = 2$.

**Answer:** 2

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