The cost price of two articles is the same. One of them is sold at a profit of 13% while the other one is sold at a profit of 19%. If the difference between their selling prices is Rs. 126, the cost price of each article is:

Correct option is D

Given:
The cost of two articles is the same
One article is sold at 13% profit
Other article is sold at 19% profit
Difference between their selling prices is Rs. 126
Formula Used:
​$$\text{SP} = \left( \frac{100 + P\%}{100} \right) \times \text{CP}$$​​
where,
SP = Selling Price
CP = Cost Price
P% = Profit Percentage
Solution:
Let the cost price of two articles be Rs. x
Since, we know that selling price = $$\left( \frac{100 + P\%}{100} \right) \times \text{CP}$$​​
=> Selling price of first article = x × (100 + 13)%
=> Selling price of first article = 1.13x
Selling price of second article = x × (100 + 19)%
=> Selling price of second article = 1.19x
Now, according to question
The difference between their selling prices = Rs. 126
=> 1.19x – 1.13x = 126
=> 0.06x = 126
=> x = $$\frac{126}{0.06}$$​ = 2100
∴ The cost price of each article is Rs. 2100.