

Direct Formula / Rule 5 :
Theorem:
n gm of sugar solution has x% sugar in it. The
quantity of sugar should be added to make it y% in the solution is given by
= n 
( 
y  x 
) 
gm. 
100  y 
or Quantity of sugar added
= 
( 
Solution (required % value  present % value) 
) 
(100  required % value) 
Example :
300 gm of sugar solution has 40% sugar in it. How
much sugar should be added to make it 50% in the
solution?
Detail Method :
300 X 40/100 = 120 gm
300  120 = 180 gm
180gm = 120 + 60 gm
so 60 gm
Ailigation Method :
The existing solution has 40% sugar. And sugar is to be mixed; so the other solution
has 100% sugar. So by alligation method:
The two mixtures should be added in the ratio 5 : 1.
Therefore, required sugar = 
300 
X 1 = 60 gm. 
5 
Quicker Method : Here you can use direct formula :
quantity of sugar added = 
300 (50  40) 
= 60 gm. 
100  50 
Exercise :

A mixture of 40 litres of milk and water contains 10%
water. How much water must be added to make 20%
water in the new mixture?

A petrol pump owner mixed leaded and unleaded petrol
in such a way that the mixture contains 10% unleaded
petrol. What quantity of leaded petrol should be added
to 1 litre mixture so that the percentage of unleaded petrol
becomes 5%.

15 litres of a mixture contains 20% alcohol and the rest
water. If 3 litres of water be mixed in it, the percentage of
alcohol in the new mixture will be:
Answers :
1 = 5 litres, 2 = 1000 ml, 3 = 16 2/3%



