Theorem:
A man mixes M_{1} litres of milk at Rs x per litre
with M_{2} litres at Rs y per litre. Amount of water, that
should be added to make the average value of the mixture Rs z per litre, is given by
=
[
M_{1}(x - z) + M_{2}(y - z)
]
litres.
z
Example :
A man mixes 5 kilolitres of milk at Rs 600 per kilolitre
with 6 kilolitres at Rs 540 per kilolitre. How many
kilolitres of water should be added to make the average
value of the mixture Rs 480 per kilolitre?
Detail Method :
According to the question,
Cost of 5 kilolitres of milk = 600 X 5 = Rs 3000
Cost of 6 kilolitres of milk = 540 X 6 = Rs 3240
Now, we suppose that x kilolitres of water is added.
Total amount of the mixture = 5 + 6 + x = (11 + x) kilolitres.
Total cost of the mixture = Rs 3000 + Rs 3240= Rs 6240
From the question.
=
6240
= 480
11 + x
or, 11 + x
6240
= 13
480
∴ x = 2 kilolitres
Ailigation Method :
Cost of milk when two qualities are mixed
=
5 X 600 + 6 X 540
= Rs
6240
per kilolitre.
5 + 6
11
Cost of water = Rs 0/ kilolitre.
So, First mixture (milk)
Second mixture (water)
6240/11
Average Speed 480
0
480
960/11
∴ Ratio of milk and water = 480 : 960/11 = 1 : 2/11 = 11 : 2
Which implies that 11 kilolitres of milk should be mixed
with 2 kilolitres of water. Thus 2 kilolitres of water
should be added.
Quicker Method : Here you can use direct formula :
The required amount of water
=
5 X (600 - 480) + 6 X (540 - 480)
480
=
5 X 120 + 6 X 60
=
960
= 2 kilolitres.
480
480
Exercise :
A man mixes 5 kilolitres of milk at Rs 6000 per kilolitre
with 6 kilolitres at Rs 5400, and with sufficient water to
make the average value Rs 4800 per kilolitre. How many
kilolitres of water has he added?
A man mixes 6 kilolitres of milk at Rs 650 per kilolitre with
7 kilolitres at Rs 600, and with sufficient water to make
the average value Rs 540 per kilolitre. How many kilolitres
of water has he added?
A man mixes 6 kilolitres of milk at Rs 325 per kilolitre with
9 kilolitres at Rs 300, and with sufficient water to make
the average value Rs 270 per kilolitre. How many kilolitres
of water has he added?