Given, 2 seller selling the good
Seller 1 claim he made 25% profit on Cost price.
Seller 2 claim he made 25% profit on selling price.
Lets selling price be y --------------------- 1
Lets take seller 2 first
He's claims that he made 25% profit on selling price.
i.e his cost price would be y - $\frac{25y}{100}$ = $\frac{75y}{100}$
Profit he made = selling price - cost price = y - $\frac{75y}{100}$ = $\frac{25y}{100}$ ---------------------- 2
Now lets take seller 1 next
He is claiming he made 25% profit on cost price, lets his cost price be x
so his selling price will become = x + $\frac{25x}{100}$ = $\frac{125x}{100}$ ----------------------- 3
Profit he made = selling price - cost price = $\frac{125x}{100}$ - x = $\frac{25x}{100}$ ----------------------- 4
From 1 and 3
Since its given selling price is same so y = $\frac{125x}{100}$ i.e x = $\frac{100y}{125}$ -------------------- 5
From 2 and 4
Its given in question there is a difference of 100 rs between profit made by both the seller so we can write
$\frac{25y}{100}$ - $\frac{25x}{100}$ = 100
25y - 25x = 10000
25y - $\left ( 25 \times \frac{100y}{125} \right )$ = 10000 (from 5)
5y = 10000
y = 2000
i.e selling price is 2000 rs
option a is correct here.