Question

In 50gm alloy of gold and silver. The gold is 80% by weight. How much gold should be mixed to this alloy so that the weight of gold would become 95%?
A.200gm
B.150gm
C.50gm
D.10gm

Answer 1

Solution:
Hint: In this type of question you should know the formula for the percentage. For example in this case the formula for percentage weight of gold can be (weight of gold/weight of alloy) $ \times $100. So during application of this formula you should confirm what is the name of the thing, metal or any other thing whose percentage is asked.

Complete step-by-step solution:
Given = total weight of alloy = $50gm$
Net weight of gold given = $80\% $
To find = Amount of gold to be added to make the composition of gold to be $95\% $
According to the question the gold is $80\% $
So $80\% $of 50gm is
$\dfrac{{80}}{{100}} \times 50 = 40gm$
If we add ‘a’ gram of gold with this alloy, composition becomes $95\% $
$
  \dfrac{{40 + a}}{{50 + a}} \times 100 = 95 \\
  4000 + 100a = 4750 + 95a \\
  5a = 750 \\
  a = \dfrac{{750}}{5} \\
  a = 150gm \\
 $
So the amount of gold to be added is $150gm$.
The correct option is B = $150gm$

Note: One can have a doubt during solving i.e. we are adding only gold to the alloy then we add ‘a’ amount in the denominator i.e. the weight of total alloy? That is because if we add gold to alloy as the amount of gold individually increases, the amount of total alloy also increases. Also while applying the formula for percentage try to make 10, 100, 1000…… in the denominator because it can help in making the calculation easy.