Question

An alloy contains $ 32\% $ copper, $ 40\% $ zinc and the rest nickel. Find in grams the quantity of each of the contents in $ 1 $ kg of alloy.

Answer 1

Hint: Here we will consider an alloy as the hundred percentage and the respective contents as the percentage given and then find the respective third content from it. Also use the conversion ratio for the kilogram to gram relation.

Complete step-by-step answer:
In $ 100\% $ an alloy contains $ 32\% $ copper, $ 40\% $ zinc and the rest nickel.
Therefore, percentage of Nickel $ = 100 - (32 + 40) $
Simplify the above expression –
Percentage of Nickel $ = 100 - 72 $
Percentage of Nickel $ = 28\% $
Now, in $ 100gm $ there will be –
Copper $ = 32\;g $
Zinc $ = 40\;g $
And Nickel $ = 27g $
We know that – One kilogram is equal to thousand gram
This can be expressed as –
 $ 1kg = 1000\;gm $
Also, $ 1000\;gm = 100 \times 10\;gm $
So, if an alloy is increased ten times, the respective contains are also increased ten times.
Therefore, now in $ 1000gm $ there will be –
Copper $ = 32\;g \times 10 $
Simplify the above expression –
$\Rightarrow$ Copper $ = 320\;g $ .... (A)
Similarly Zinc $ = 40\;g \times 10 $
Simplify the above expression –
$\Rightarrow$ Zinc $ = 400\;g $ .... (B)
And Nickel $ = 28\;g \times 10 $
Simplify the above expression –
$\Rightarrow$ Nickel $ = 280\;g $ .... (C)
From equations (A), (B) and (C)
Hence, $ 1 $ kg of alloy contains copper $ 320\;g, $ Zinc $ 400\;g $ and Nickel $ 280\;g. $
So, the correct answer is “$ 320\;g, $ Zinc $ 400\;g $ and Nickel $ 280\;g. $”.

Note: The above example can be solved by another method.
First assume any variable as the alloy and convert the given percentage in the form of decimals of the variable and then solve accordingly. Know the basic conversational relation and convert the units from one form to another.