An alloy contains 40% of silver, 30% of copper, and 30% of nickel. How much silver (in kg) should be added to 25 kg of the alloy so that the new alloy contains 50% of silver?

Shortcut Trick

Silver = 40%; Copper = 30%; Nickel = 30%

Let, the total weight of alloy = 100 units

So, the silver = 40 units

If we add 20 units silver then, alloy = (100 + 20) = 120 units

also, silver = 40 + 20 = 60 units

Now, silver is 50% of the alloy  [∵ silver = 60 and alloy = 120]

So, 100 units = 25 kg

⇒ 20 units = (25/100) × 20 = 5 kg

∴ A total of 5 kg silver (in kg) should be added to 25 kg of the alloy so that the new alloy contains 50% of silver.

Alternate Method

Given:

An alloy contains 40% of silver, 30% of copper, and 30% of nickel.

Total weight of the alloy = 25 kg

The required percentage of silver = 50%

Calculation:

The ratio of silver, copper and nickel = 40 : 30 : 30 = 4 : 3 : 3

Let, total silver = 4x; copper = 3x; and nickel = 3x

So, 4x + 3x + 3x = 25

⇒ 10x = 25

⇒ 4x = (25/10) × 4 = 10

The weight of silver in 25 kg = 10 kg

Suppose, the amount of silver added = a kg

Then, (10 + a) = 1/2 (25 + a)  [∵ 50% = 1/2]

⇒ 20 + 2a = 25 + a

⇒ 2a - a = 25 - 20

⇒ a = 5

∴ A total of 5 kg silver (in kg) should be added to 25 kg of the alloy so that the new alloy contains 50% of silver.