Calculate the weight and the percentage of zinc in the zinc-copper alloy being given that the latter's alloy with 3 kg of pure zinc contains 90 per cent of zinc and with 2 kg of 90% zinc alloy contains 84% of zinc.

Hi Let us say alloy has x kg of Zinc and y kg of Cu Now from 1st case we can say : we add 3kg of pure Zn to alloy so we get total zinc as x+3 and cu as y now by condition we get (x+3)/y =9/1 we get 9y-x=3 ....(1) Now 2Kg of 90% alloy means 1.8Kg Zinc and 0.2 Kg Cu Now by condition (x+1.8)/x+y+2 =84/100 25x+45=21x+21y+42 or 21y-4x=3 ...(2) equating 1 and 2 we get 21y-4x=9y-x so we get 12y =3x or x =4y Now percentage of Zinc = (x/x+y)*100 so we get 4/5*100 =80% We have 9y-x=3 so 5y=3 or y=0.6 so x=2.4 Therefore weight of Zinc =2.4 Kg

Sir, wouldnt it be (x+3)/y = 9/10 and we get 9y-10x = 30 instead ?

Hi Rishi Thank you for pointing out , by mistake I took 10 it would be 1 only as we are comparing with copper so equation would be x+3/y =9 so we get 9y-x=3. 9/10 would be x+3/x+3+y , equating that would also be 9y-x=3.