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?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 20%
Total Cost Price (CP) = \( 400 \times 60 = 24000 \)
To gain 12%, total Selling Price (SP) must be: \( SP = 24000 + \frac{12}{100} \times 24000 = 24000 + 2880 = 26880 \)
SP of first 200 m (with 4% gain) = \( 200 \times 60 + \frac{4}{100} \times 200 \times 60 = 12000 + 480 = 12480 \)
Let required SP of remaining 200 m be \( x \). Then, total SP = \( 12480 + x \)
\( 12480 + x = 26880 \Rightarrow x = 26880 - 12480 = 14400 \)
CP of remaining 200 m = \( 200 \times 60 = 12000 \)
Profit on second half = \( 14400 - 12000 = 2400 \)
Required percentage = \( \frac{2400}{12000} \times 100 = 20\% \)