Theorem:
If M kg of mixture, of which is a/b and the rest
is B, be mixed with N kg of metal, of which is x/y and the
rest is B, then the ratio of A to B in the mixture is given by
=
[
M
a
+ N
x
b
y
]
M
(
1 -
a
)
+ N
(
1 -
x
)
b
y
Example :
If 2 kg of metal, of which 1/3 is zinc and the rest of copper, be mixed with 3 kg of metal, of which 1/4 is
zinc and the rest is copper, what is the ratio of zinc to
copper in the mixture?
Detail Method :
Quantity of zinc in the mixture
= 2(1/3)+3(1/4) = 2/3+3/4 = 8+9/12 = 17/12
Quantity of copper in the metal
= 3+2-17/12 = 5-17/12 = 43/12
So ratio = 17/12 : 43/12 = 17 : 43
Quicker Method : Here you can use direct formula :
the required ratio
=
[
2 X
1
+ 3
1
3
4
]
2
(
1 -
1
)
+ 3
(
1 -
1
)
3
4
=
2/3 + 3/4
= 17 : 43.
4/3 + 9/4
Exercise :
If 1 kg of metal of which 1/3 is zinc and the rest copper be
mixed with 2 kg of metal of which 1/4 is zinc and the rest
copper, what is the ratio of zinc to copper in the mixture?
If 4 kg of metal of which 1/4 is zinc and the rest copper be
1 mixed with 5 kg of metal of which 1/5 is zinc and the rest
copper, what is the ratio of zinc to copper in the mixture?
If 5 kg of metal of which 3/5 is zinc and the rest copper be
mixed with 3 kg of metal of which 2/3 is zinc and the rest
copper, what is the ratio of zinc to copper in the mixture?