A costs thrice as much as B. A is sold at a loss of 10%, and B is sold at 5/4 of its own price. If the selling price of A is Rs. 5,800 more than the selling price of B, then the cost price of A is:

Correct option is B

Given:
A costs thrice as much as B.
Selling of A is done at 10% loss and B is sold at 5/4 of its own price.
Selling price of A is Rs 5800 more than SP of B.
Formula Used:
Selling Price =  $$\frac{(100-Loss \%)}{100}×CP$$​​
Solution:
Let the cost of B be x.
So, cost of A = 3x
Selling price of B =  $$\frac{5x}{4}$$​​
Selling price of A when 10% loss is there = $$\frac{(100-10)}{100}×3x$$​​
Selling price of A with 10% loss = 2.7x →(1)
Also, as per the second condition,
SP of A = $$\frac{5x}{4}$$​+5800 →(2)
Equating both the equations, we get
​$$\frac{5x}{4}+5800=2.7x \\\ \\\frac{5x}{4}-2.7x=-5800 \\\ \\\frac{(5x-2.7x×4)}{4}=-5800 \\\ \\5x-10.8x=-5800×4 \\\ \\-5.8x=-23200 \\\ \\x=\frac{(-23200)}{(-5.8)}=Rs 4,000$$​​
So, Cost price of A = 3x = 3 × 4000 = Rs 12,000