Theorem:
A trader has N kg of certain item, part of which
he sells at x% profit and the rest at y% profit. He gains P%
on the whole.
The quantity of item sold at x% profit is =
(
y - P
)
N Kg
y - x
and the quantity of item sold at y% profit is =
(
P - x
)
N Kg
y - x
Example :
A trader has 50 kg ofpulses, part of which he sells at
8% profit and the rest at 18% profit. He gains 14% on
the whole. What is t e quantity sold at 18% profit?
Detail Method :
Let the quantity sold at 18% profit be x kg. Then the
quantity sold at 8% profit will be (50 - x) kg.
For a matter of convenience suppose that the price of
pulse is 1 rupee per kg.
Then price of x kg pulse = Rs x and price of (50 - x) kg
pulse = Rs (50 - x)
Now we get an equation,
18% of x + 8% of (50 - x)= 14% of 50
18x + 8(50 - x) = 14 X 50
10x = 300
∴ x = 30
Ailigation Method :
I Part
II Part
8% profit
mean profit 14%
18% profit
4%
6%
= 4 : 6 = 2 : 3
Therefore the quantity sold at 18% profit
=
50
X 3 = 30 kg,
2 + 3
Quicker Method : Here you can use direct formula :
the required quantity =
(
14 - 8
)
X 50
18 - 8
=
6
X 50 = 30 kg.
10
Exercise :
A trader has 25 kg of rice, part of which he sells at 4%
profit and the rest at 9% profit. He gains 7% on the
whole. What is the quantity sold at 9% profit?
A trader has 100 kg of wheat, part of which he sells at
16% profit and the rest at 36% profit. He gains 28% on
the whole. What is the quantity sold at 36% profit?
A trader has 40 kg of pulses, part of which he sells at
10% profit and the rest at 20% profit. He gains 16% on
the whole. What is the quantity sold at 20% profit?