Solve and Produce a Clean Re-written Version

ROLE: Act as a mathematics teacher and editor who turns a messy or poorly printed question into a clean, professional version, then solves it.

CONTEXT: I teach [CLASS/GRADE] for [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET], topic [TOPIC]. The question in my photo is messy, faded, or badly formatted, and I want a tidy re-written version I can put in a worksheet, plus the solution.

YOUR TASK:
1. Read the question in the attached photo precisely.
2. Re-write it as a clean, well-formatted, exam-ready question - improving only wording, spacing, and presentation, NOT the mathematics.
3. Keep every number, condition, and instruction exactly the same in meaning.
4. Then solve the question fully.

INPUT: I have attached a photo of the problem. If any part is unclear, tell me which symbol or line you cannot read, state your best assumption, and continue. Do not alter any quantity or condition while cleaning it up.

HOW TO WORK IT OUT: After re-writing, solve the problem silently. Then VERIFY the final answer with TWO independent checks (for example substitute back, and re-derive a second way). If the checks disagree, fix the error before replying. Confirm your clean version is mathematically identical to the original. Never invent formulas or values; name standard results. Keep all mathematics fully legible in clean LaTeX or clear plain text, one step per line.

OUTPUT FORMAT (use these exact headings):
1. Original as I read it - the question straight from the photo.
2. Clean re-written version - tidy, exam-ready wording, same maths.
3. Confirmation - one line stating the maths is unchanged from the original.
4. Step-by-step solution - numbered, one idea per line, short reasons.
5. Final answer - clearly stated.
6. Verification - Check 1 and Check 2, each in one or two lines.

RULES: Improve presentation only; never change the problem's meaning, numbers, or conditions. If you must guess a faded number, flag it clearly. Use plain ASCII only with straight quotes. Be exact unless an estimate is requested.

FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return the complete material as a clean, print-ready A4 handout that can be pasted into Word or Google Docs and saved as PDF. Use a clear title, logical sections, readable mathematics and page-break markers where needed. Keep student material separate from the answer key or teacher notes.


MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.
At the very end add a footer line: "Prepared by [YOUR NAME]", and put "Compiled by [YOUR NAME]" in the title or header block at the top.

CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.

GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.

SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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🔗 Free tools & to reach me: https://jee-prompt-studio.pages.dev/
Questions, feedback or appreciation are always welcome.
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