A ₹54,000 grant is distributed among Research, Teaching, and Administration in a 6:8:4 ratio. Teaching department uses ₹5,000 for equipment and ₹3,000 for books, then distributes the rest to four faculty members in a 4:3:2:1 ratio. How much does the faculty member with the smallest share receive?

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1. Split ₹54,000 in ratio 6:8:4. Total parts = $6+8+4=18$, so one part = $54000/18=3000$.  
2. Teaching share = $8	imes3000=24000$.  
3. After ₹5,000 for equipment and ₹3,000 for books, left = $24000-5000-3000=16000$.  
4. Four faculty share 16000 in ratio 4:3:2:1 (sum = 10). Smallest share = $16000/10=1600$.

FINAL_ANSWER: a

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