Four students A, B, C, and D appeared for an English exam consisting of two sections: Short questions and Long questions.
**Short questions:** - Each question carries 5 marks. - Candidates must attempt at least 6 out of every 7 questions. - Total short questions: 42.

**Long questions:** - Each question carries 10 marks. - Candidates must attempt at least 7 out of every 9 questions. - Total long questions: 18.

**Penalty:** - 0.5 marks deducted for each spelling error. - 0.75 marks deducted for each full word missed.
Details: - B answered 14 long questions correctly and scored 131 marks in the long section. - B scored 175 marks in the short section. - A scored 160 marks in the short section by attempting 38 questions. - C attempted all short questions and scored 150.5 marks in the long section. The number of short questions C answered correctly is twice the number of long questions he answered correctly. - D answered 15 long questions correctly. - The ratio of spelling errors in D's long to short sections is 3:4. - B made 43 spelling errors and 18 full word errors in the short section. - The total number of spelling errors made by D equals the total number of questions B answered correctly.

**Question:** If D answered 40 short questions correctly, what is the total marks obtained by D in both sections?

Question

Four students A, B, C, and D appeared for an English exam consisting of two sections: Short questions and Long questions.
**Short questions:** - Each question carries 5 marks. - Candidates must attempt at least 6 out of every 7 questions. - Total short questions: 42.

**Long questions:** - Each question carries 10 marks. - Candidates must attempt at least 7 out of every 9 questions. - Total long questions: 18.

**Penalty:** - 0.5 marks deducted for each spelling error. - 0.75 marks deducted for each full word missed.
Details: - B answered 14 long questions correctly and scored 131 marks in the long section. - B scored 175 marks in the short section. - A scored 160 marks in the short section by attempting 38 questions. - C attempted all short questions and scored 150.5 marks in the long section. The number of short questions C answered correctly is twice the number of long questions he answered correctly. - D answered 15 long questions correctly. - The ratio of spelling errors in D's long to short sections is 3:4. - B made 43 spelling errors and 18 full word errors in the short section. - The total number of spelling errors made by D equals the total number of questions B answered correctly.

**Question:** If D answered 40 short questions correctly, what is the total marks obtained by D in both sections?

Accepted Answer

**Solution:**

1. Calculate the number of short questions B answered correctly:
   - B's short section marks = 175
   - B's spelling errors = 43
   - B's full word errors = 18

Total marks before penalty for short questions:
   $$	ext{Correct marks} = 175 + (43 	imes 0.5) + (18 	imes 0.75)$$
   $$= 175 + 21.5 + 13.5 = 210$$

Since each short question carries 5 marks:
   $$	ext{Number of correct short questions by B} = \frac{210}{5} = 42$$

2. Total questions B answered correctly (short + long):
   $$42 + 14 = 56$$

3. Total spelling errors made by D equals total questions B answered correctly:
   $$	ext{Spelling errors by D} = 56$$

4. Ratio of spelling errors by D in long to short sections is 3:4:
   - Let spelling errors in long section = $3x$
   - Spelling errors in short section = $4x$

Since total spelling errors = 56:
   $$3x + 4x = 56 \Rightarrow 7x = 56 \Rightarrow x = 8$$

So,
   - Spelling errors in long section = $3 	imes 8 = 24$
   - Spelling errors in short section = $4 	imes 8 = 32$

5. Calculate marks obtained by D:
   - Long section:
     - Correct answers = 15
     - Marks before penalty = $15 	imes 10 = 150$
     - Penalty for spelling errors = $24 	imes 0.5 = 12$
     - Marks after penalty = $150 - 12 = 138$

- Short section:
     - Correct answers = 40
     - Marks before penalty = $40 	imes 5 = 200$
     - Penalty for spelling errors = $32 	imes 0.5 = 16$
     - Marks after penalty = $200 - 16 = 184$

6. Total marks obtained by D:
   $$138 + 184 = 322$$

**Answer:** 322

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