Half of the 100 articles sold at a profit of 20% and the rest at a profit of 40%. If all the articles had been sold at a profit of 25%, the total profit would have been Rs. 100 less than earlier profit. The cost price of each article was

Assume cost price of each article be 'x'

According to question,

50 articles sold at a profit of 20% = $$ \frac{50x \times 120}{100} $$

50 articles sold at a profit of 40% =$$ \frac{50x \times 140}{100} $$

If all the articles sold at 25% = $$ \frac{100x \times 125}{100} $$ , the total profit would have been Rs. 100 less than earlier profit.

Substituting,

$$ \frac{50x \times 120}{100} + \frac{50x \times 140}{100} - \frac{100x \times 125}{100} = 100 $$

60x + 70x - 125x = 100

130x - 125x =100

5x = 100

x = $$ \frac{100}{5} =20 $$