A shop wants to sell a certain quantity of grains. it sells half of the quantity and an additional 3 kg of these grains to the first customer. then it sells half of the remaining quantity and an additional 3kg of these grains to the second customer. finally when the shop sells half of the remaining quantity and an additional weights 3 kgs of these grains to the third customer, there are no grains left. the initial quantity, in kgs of grains are

Let us assume that there are x kg of grain at the start
Amount of grain given to 1 person is= 0.5x+3 kg
So, the amount of grain remaining is= x-(0.5x+3)=0.5x-3 kg
Now, the amount of grains given to the second person is: 0.5(0.5x-3)+3
So, the amount of grains remaining is= (0.5x-3)-[0.5(0.5x-3)+3] =0.5(0.5x-3)-3 kg
Now, the amount of grain given to the third person is= 0.5[0.5(0.5x-3)-3]+3
Then the amount of grain remaining will be=0.5[0.5(0.5x-3)-3]-3=0 [no grains remain in the end]
0.5[0.5(0.5x-3)-3]-3=0
0.5(0.5x-3)-3=6
0.5x-3=18
0.5x=21
x=42 kg