Answer is b) 13.4 %
Given:
SP = 1134
discount = 19 %
The key point here is that discount is always given on marked price (MP) but luckily the question mentions that.
Let the MP be x
So, SP = MP - discount
1134 = x - $\frac{19}{100}$ x
x = 1400 i.e. marked price = 1400
The question says had he not given the discount he would have earned a profit of 40% on the cost price. So had he not given the discount, the CP would be same as MP.
So we now have, CP = 1400 and profit = 40 %
$\therefore$ SP = CP + Profit = CP + $\frac{40}{100}$ CP (Profit/Loss is always calculated on CP)
$\therefore$ CP = 1000 and given that SP = 1134
%Profit = $\frac{1134 - 1000}{1000}$ * 100 = 13.4