On selling 140 articles for ₹360 a person bears a loss of 36%. How many articles should he sell for ₹198 to earn a profit of 54%?

32

36% = \(\frac{36}{100}\) = \(\frac{9}{25}\),  54% = \(\frac{54}{100}\) = \(\frac{27}{50}\)

At 36% loss:-

In Rs. 360, no. of articles sold = 140

In Rs. 198, no. of articles sold = \(\frac{140}{360}\) × 198

No. of articles sold for Rs. 198 to cover the loss = \(\frac{140}{360}\) × 198 × \(\frac{16}{25}\) 

No. of articles sold for Rs. 198 to gain 54% = \(\frac{140}{360}\) × 198 × \(\frac{16}{25}\) × \(\frac{50}{77}\) = 32 articles