A jeweler mixed gold and copper in two proportions. In type A alloy, 6 gm gold…
2022
A jeweler mixed gold and copper in two proportions. In type A alloy, 6 gm gold is mixed with 5 gm copper and in type B alloy, 5 gm gold is mixed with 3 gm copper. If the jeweler mixed 122 gm gold and 90 gm copper, then find the weight of type B alloy.
- A.
80 gm
- B.
60 gm
- C.
70 gm
- D.
100 gm
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept
In a fixed-ratio mixture (alloy), each constituent is a fixed fraction of every batch. If you mix a quantity of one alloy and a quantity of another, the total of each constituent is the sum of its contributions from both alloys. So two unknown alloy quantities can be found by writing one linear equation per constituent and solving the simultaneous pair.
Application
Type A is gold:copper = 6:5, so one A-batch = 6 + 5 = 11 gm. Type B is gold:copper = 5:3, so one B-batch = 5 + 3 = 8 gm. Let a = number of A-batches and b = number of B-batches.
Gold equation (total gold = 122): 6a + 5b = 122.
Copper equation (total copper = 90): 5a + 3b = 90.
Eliminate b: multiply the gold equation by 3 and the copper equation by 5 to get 18a + 15b = 366 and 25a + 15b = 450. Subtract: 7a = 84, so a = 12.
Substitute a = 12 into 5a + 3b = 90: 60 + 3b = 90, so 3b = 30 and b = 10.
Weight of type B alloy = b x 8 = 10 x 8 = 80 gm.
Cross-check
Weight of type A alloy = a x 11 = 12 x 11 = 132 gm. Total alloy = 132 + 80 = 212 gm, which equals total gold + total copper = 122 + 90 = 212 gm. Gold used = 6(12) + 5(10) = 72 + 50 = 122 and copper used = 5(12) + 3(10) = 60 + 30 = 90, matching the given amounts exactly.
Therefore the weight of type B alloy is 80 gm.