

Direct Formula / Rule 24 :
Theorem:
There is a cask which contains 'L' litres of milk
as cost price Rs x/litre. The amount of water, which should
be added to the cask so that the cost of milk reduces to Rs y/litre, is given by
Example :
How much water must be added to a cask which contains
40 litres of milk at cost price Rs 3.5/litre so that
the cost of milk reduces to Rs 2/litre?
Detail Method :
Let the x litres of water be added to
the the cask.
Cost price of 40 litres of milk = 40 X 3.5 = Rs 140.
According to the question,
= 
140 
= 2 or, 2x = 140  80 = 60 
40 + x 
So x = 30 litres.
Ailigation Method :
We will apply the alligation on
price of milk, water and mixture.
∴ ratio of milk and water should be 2 : 1.5 = 4 : 3.
∴ added water = 40/4 X 3 = 30 litres.
Quicker Method : Here you can use direct formula :
required amount of water
= 
40 
[ 
3.5  2 
] 
= 40 X 3/4 = 30 litres. 
2 
Exercise :

How much water must be added to 14 kilolitres of milk
worth Rs 5.40 a litre so that the value of the mixture may
be Rs 4.20 a litre?

How much chicory at Rs 24 a kg should be added to 15
kg of tea at Rs 60 a kg, as to make the mixture worth Rs 39
a kg?

How many bananas at 5 for Rs. 1.20 should be mixed with
300 bananas at 6 for Rs 2.10 so that they should all be
worth Rs 3.60 a dozen?
Answers :
1 = 4 kilolitres, 2 = 21 kg, 3 = 250



