Q. An alloy of copper and zinc contains……….% copper by weight. ‘X’ kg of zinc is added to the mixture which makes zinc 33 1/3% by weight. If ‘X’ Kg of copper would have been added instead, the percentage of Cu by weight would be 83 1/3%. If 3X Kgs zinc would have been added, the percentage of zinc will become…………The ratio of the weight of the original mixture to X is 5:1.
A) 80%, 50%
B) 50%, 80%
C) 75%, 60%
D) 60%, 75%
E) None of these
Sol:
Let the weight of copper and zinc be ‘a’ and ‘b’respectively.
X’ kg of zinc is added to the mixture which makes zinc 33 1/3% by weight
=> (b+X)/(a+b+X)=1/3
=> 3b+3X=a+b+X
=> 2b=a-2X
=> a=2b+2X —————————(1)
Again, if X Kg of copper would have been added
instead, the percentage of Cu by weight would
be 83 1/3%.
=> (a+X)/(a+b+X)=5/6
=> 6a+6X=5a+5b+5X
=> a=5b-X —————————(2)
Ratio of weight of original mixture and X is 5:1
=> (a+b)/X=5
=>a+b=5X
=> a= 5X-b ——————————-(3)
Using (2) and (3), we get
5b-X=5X-b
=> 6b=6X
=> b=X
From (1) and (2), we get
2b+2X=5b-X
=> 3b=3X
=> b=X
From (3), we get
a=5b-b=4b
=> a=4b
If 3X Kgs zinc would have been added,
Percentage of zinc=
(b+3X)/(a+b+3X)*100%=(b+3b)/(4b+b+3b)*100=
4b/8b*100%=
50%
Also, initial weight of copper by
%=a/(a+b)*100%=4b/5b*100=80%
