An article is sold at a profit of $13 \frac{1}{4} \%$. Had it been sold for $Rs. 76.70$ more, the profit would have been $16 \frac{1}{5} \%$. 50% of the cost price of the article (in Rs.) is:

1,300

Let the CP be 100x.

So, SP = 113.25x     [ 13\(\frac{1}{4}\) % = 13.25%]

New, SP = 116.2x     [16\(\frac{1}{5}\) % = 16.2%]

According to the question,

116.2x -  113.25x = 76.7

⇒ 2.95x = 76.7

⇒ x = \(\frac{76.7}{2.95}\)  = 26

So,  CP = 100 × 26

⇒ Rs. 2600

50% of CP = 1300