Puzzle about measuring difference in weights

Q. Ali the thief had managed to break into the Sultan's treasure room. He was looking for a bag containing 1250 diamonds, each weighing 0.8 grams. Unfortunately, the Sultan had filled nine other bags with imitation diamonds. There were 1000 in each bag, each one weighing 1 gram. So all 10 bags weighed exactly 1000 grams and all the bags looked exactly alike. Just as Ali was scratching his head, the Sultan burst in with his guards. As he was a merciful Sultan, he gave Ali a chance to save his life. Here is what he said; "If you can find the bag which contains the real diamonds by using these scales just once, you may keep the diamonds. If not, you will be beheaded. You can take
stones from any of the bags and put them in other bags if you wish but you can only weigh once!" How did Ali save his neck?

Ans: Ali numbered the ten bags from 1 to 10. He then took ten stones from bag 1, twenty stones from bag 2, thirty stones from bag 3 .... likewise till hundred stones from bag 10 and weighed them together. Had all the stones weighed 1 gm in all ten bags, the total weight would have been 550 grams. since one of the bags had real diamonds of lesser weight ( by 0.2 gm each ), Ali had lesser weight than 550 gms. If Ali had the weight measured as 548 gms, bag 1 from which Ali had taken ten stones contained real diamonds. If the weight had been 546 gms, bag 2 had real diamonds etc. Thus he knew which bag contained the real diamonds by the measured weight by measuring only once.