Question

An alloy of copper and bronze weight 50g. It contains 80% copper. How much copper should be added to the alloy so that percentage of copper is increased to 90%?

Answer 1

Hint: There are more than one method to find the solution. We will apply Unitary Method. Find out 80% of 50g to know about the quantity of copper in the alloy. Then 1% , after that we can easily find out 90%.

Complete step-by-step answer:
An alloy of copper and bronze weight 50g. It contains 80% copper
Quantity of copper in gram in the alloy = $ 80 \%$ \[ \times \] 50
                                                                       = $\dfrac{{80}}{{100}} \times 50$
                                                                       = 40g
Now apply Unitary Method
If 80% of copper = 40g
Then, 1% of copper = \[\dfrac{{40}}{{80}}\]
90 % of copper = $\dfrac{{40}}{{80}} \times 90$ = 45g
Therefore, 5g of copper should be added to the alloy so that percentage of copper is increased to 90%.

Note: Alternative method
As we know that 100% means ‘all of it , the whole thing. So, there is an alloy of 50g. In terms of percentage, 50g is equal to 100%. The units are different but it means the same thing.
$\because $ 100% = 50g
By using Unitary Method
1% = $\dfrac{{50}}{{100}}$
90% = \[\dfrac{{50}}{{100}} \times 90\]
= 45g
Now we will find out how much copper was there in 50g when there is 80% of copper in alloy.
 Quantity of copper in gram in the alloy = $80{\raise0.5ex\hbox{$\scriptstyle 0$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 0$}} \times 50$
                                                                       = $\dfrac{{80}}{{100}} \times 50$
                                                                       = 40 g
This means there should be an addition of 5g to the alloy so that percentage of copper is increased to 90%.