

Direct Formula / Rule 18 :
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 
( 
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+217/12 = 517/12 = 43/12
So ratio = 17/12 : 43/12 = 17 : 43
Quicker Method : Here you can use direct formula :
the required ratio
= 
[ 

] 
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?
Answers :
1 = 5 : 13, 2 = 2 : 7, 3 = 5 : 3



