Question

a Jeweller has bars of 18 carat gold and 12 carat gold how much of each must be melted together to obtain a bar of 16 carat gold weighing 120 gram. (given:pure gold is 24 carat gold)????

Answer 1

Percentage of gold in 18-carat gold = (18/24×100)%= 75% Percentage of gold in 12-carat gold=(12/24×100)%=50% Percentage of gold in 16-carat gold=(16/24×100)%=200/3% Let x gm of 18-carat gold and y gm of 12-carat gold be mixed. Thus x+y=120          -1 And ,75% of x + 50% of y=200/3% of 120 75/100x + 50/100y= 200/3×120 Multiply both sides by 100 75x + 50y=8000 Divide both sides by 25,we get 3x+ 2y=320              -2 Multiplying-1 by 3, we get 3x+3y=360               -3 Subtracting -2 from -3,we get y=40 Substitute y=40 in -1 , we get  x+40=120 x=120-40 x=80 Thus 80 gms of 18-carat gold should be mixed with 40 gms of 12-carat gold to obtain 120 gms of 16-carat gold -----------------------------------------------------------------