Theorem:
A vessel of L litres is filled with liquid A and B.
x% of A and y% of B is taken out of the vessel. It is found
that the vessel is vacated by z%. Then the initial quantity of liquid A and B is given by
=
(
z - y
)
L litres and
(
x - z
)
L litres respectively.
x - y
x - y
Example :
A vessel of 80 litres is filled With milk and water, 70%
of milk and 30% of water is taken out of the vessel. It
is found that the vessel is vacated by 55%. Find the
initial quantity of milk and water
Detail Method :
Let the initial quantity of milk be x litres. Therefore, initial quantity of water = (80 - x) litres.
According to the question,
70% of x + 30% of (80 - x) = 55% of 80
or, 70x + 2400 - 30x = 4400
or, 40x = 2000
x = 50 litres.
Initial quantity of water = (80 - 50) = 30 litres,
Ailigation Method :
Here the % values of milk and water that
is taken from the vessel should be taken into consideration.
Milk
Water
(as there is loss on
the whole)
70%
55%
30%
25%
15%
= 5 : 3
Ratio of milk to water = 5 : 3
quantity of milk =
80
X 5 = 50 litres.
5 + 3
and quantity of water =
80
X 3 = 30 litres.
5 + 3
Quicker Method : Here you can use direct formula :
Initial quantity of milk =
(
55 - 30
)
X 80 =
25
X 80 = 50 litres.
70 - 30
40
Initial quantity of water =
(
70 - 55
)
X 80 =
15
X 80 = 30 litres.
70 - 30
40
Exercise :
A vessel of 120 litres is filled with milk and water. 80% of
milk and 40% of water is taken out of the vessel. It is
found that the vessel is vacated by 65%. What is the
ratio of milk to water?
A vessel of 40 litres is filled with milk and water. 75% of
milk and 35% of water is taken out of the vessel. It is
found that the vessel is vacated by 60%. Find the initial
quantity of milk and water.
A vessel of 80 litres is filled with milk and water. 65% of
milk and 25% of water is taken out of the vessel. It is
found that the vessel is vacated by 50%. Find the initial
quantity of milk and water.