An alloy of zinc and copper contains the metals in the ratio 5 : 3. The…
2025
An alloy of zinc and copper contains the metals in the ratio 5 : 3. The quantity of zinc to be added to 16 kg of the alloy so that the ratio of the metal may be 3 : 1 is:
- A.
2 kg
- B.
4 kg
- C.
3 kg
- D.
8 kg
Attempted by 7 students.
Show answer & explanation
Correct answer: D
Solution: Find the amount of zinc to add so the zinc:copper ratio becomes 3:1.
Given:
The alloy has zinc:copper = 5:3 and total mass = 16 kg.
Initial zinc mass = (5/8) × 16 = 10 kg.
Let x kg be the zinc added. New total mass = 16 + x. To have zinc:copper = 3:1, zinc must be 3/4 of the total.
Set up the equation: 10 + x = (3/4)(16 + x).
Solve without decimals by multiplying both sides by 4: 4(10 + x) = 3(16 + x).
That gives 40 + 4x = 48 + 3x ⇒ 4x − 3x = 48 − 40 ⇒ x = 8 kg.
Check: After adding 8 kg, zinc = 10 + 8 = 18 kg and total = 24 kg, so zinc fraction = 18/24 = 3/4, i.e. ratio 3:1.
Therefore, 8 kg of zinc should be added.