Question

Two alloys A and B contain copper and zinc in the ratio 7 : 2 and 5 : 3 respectively. How many kg of A and B must be melted in order to get an alloy of 44 kg containing copper and Zinc in the ratio 3 : 1?

• A. 24 kg, 20 kg
• B. 30 kg, 14 kg
• C. 28 kg, 16 kg
• D. 36 kg, 8 kg

Answer 1

Answer:

B. 30 kg, 14 kg

Solution: Solution: Given: Ratio of copper to zinc in alloy A = 7 : 2 Ratio of copper to zinc in alloy B = 5 : 3 Quantity of final alloy formed = 44 kg Ratio of copper to zinc in final mixture = 3 : 1 Calculation: Let x liters is added from alloy A and y liters is added from alloy B. Then (7x/9) + (5y/8) / (2x/9) + (3y/8) = 3 / 1 ⇒ (7x/9) + (5y/8) = (6x/9) + (9y/8) ⇒ [(7x-6x)/9] = [(9y-5y)/8] ⇒ (x/9) = (4y/8) ⇒ (x/y) = (9/2) ⇒ x : y = 9 : 2 Quantity taken from alloy A = (44/11) × 9 ⇒ 4 × 9 ⇒ 36 kg Quantity taken from alloy B = (44/11) × 2 ⇒ 4 × 2 ⇒ 8 kg ∴ 36 kg added from alloy A and 8 kg added from alloy B