A man bought 400 m of fabric @ Rs. 60 per metre. He sold 50% of it at a profit of 4%. At what percent should he sell the remaining to gain 12% on the whole transaction?

Total fabric purchased: 400 metres at Rs. 60 per metre

Total Cost Price $= 400 \times 60$

$= \text{Rs. } 24,000$

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Target profit on the whole transaction: 12%

Target Selling Price $= 24,000 \times 1.12$

$= \text{Rs. } 26,880$

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First half sold: 50% of 400 m $= 200$ m

Cost Price of 200 m $= 200 \times 60$

$= \text{Rs. } 12,000$

Profit on first half: 4%

Selling Price of first half $= 12,000 \times 1.04$

$= \text{Rs. } 12,480$

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Remaining fabric: 200 m

Cost Price of remaining 200 m $= 200 \times 60$

$= \text{Rs. } 12,000$

Total money needed $= \text{Rs. } 26,880$

Money already collected $= \text{Rs. } 12,480$

Required Selling Price for remaining fabric $= 26,880 - 12,480$

$= \text{Rs. } 14,400$

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Profit on remaining fabric $= 14,400 - 12,000$

$= \text{Rs. } 2,400$

Profit percentage $= \dfrac{2,400}{12,000} \times 100$

$= 20\%$

Therefore, the remaining fabric should be sold at 20% profit.