Alligation or Mixture problems
A piece of an alloy of two metals (A and B) weighs 15 gms and costs Rs. 150. If the weights of the two metals be interchanged, the new alloy would be worth Rs. 120. If the price of metal A is Rs. 6 per gm, find the weight of the other metal in the original piece of alloy.
If the two alloys are mixed, the mixture would contain 15 gms of each metal and it would cost Rs. (150 + 120) = Rs. 270. Cost of (15 gms of metal A + 15 gms of metal B) = Rs. 270 Cost of (1 gm of metal A + 1 gm of metal B) = Rs. (270 / 15) = Rs. 18 Cost of 1 gm of metal B = Rs. (18 ? 6) = Rs. 12 Average cost of original piece of alloy = (150 / 15) = Rs. 10 per gm. Quantity of metal / A Quantity of metal B = (2 / 4) = (1 / 2) Quantity of metal B = 2 (1 + 2) × 15 = 10 gms.