Theorem:
A trader has N kg of a certain item, a part of
which he sells at x% profit and the rest of y% loss. He gains
P% on the whole
Then the quantity sold at x% profit is =
(
P + y
)
N Kg
x + y
and the quantity sold at y% loss is =
(
x - P
)
N Kg
x + y
Example :
A trader has 50 kg of rice, a part ofwhich he sells at 10% profit and the rest at 5% loss. He gains 7% on
the whole. What is the quantity sold at 10% gain and
5% loss?
Detail Method :
Let the quantity sold at 10% profit be
x kg.
Then the quantity sold at 5% loss will be (50 - x) kg.
For a matter of convenience suppose that the price of
rice is 1 rupee per kg.
Then price of x kg rice = Rs x and price of (50 - x) kg
rice = Rs (50 - x)
Now we get an equation,
10% profit of x + 5% loss of (50 - x) = 7% gain of 50
or, 10% of x - 5% of (50 - x) = 7% of 50
or, 10x-250 +5x =350
∴ x = 40 kg and (50 - x)= 50 - 40 = 10 kg.
Therefore, the quantity sold at 10% profit = 40 kg and
the quantity sold at 5% loss = 50 - 40 = 10 kg.
Ailigation Method :
I Part
II Part
10
7
(-)5
12
3
Ratio of quantities sold at 10% profit and 5% loss
= 12 : 3 = 4 : 1
Therefore, the quantity sold at 10% profit
=
50
X 4 = 40 kg,
4 + 1
and the quantity sold at 5% loss = 50 - 40 = 10 kg. Note: Whenever there is loss, take the negative value. Here,
difference between 7 and (-5) = 7 - (-5) = 7 + 5 = 12.
Never take the difference that counts negative value.
Quicker Method : Here you can use direct formula :
Quantity sold at 10% profit =
(
7 + 5
)
X 50
10 + 5
=
12
X 50 = 40 kg.
15
Quantity sold at 5% loss =
(
10 - 7
)
X 50 = 10 kg.
10 + 5
Exercise :
A trader has 90 kg of pulse, a part of which he sells at
20% profit and the rest at 10% loss. He gains 14% on the
whole. What is the quantity sold at 20% gain and 10%
loss?
A trader has 45 kg of wheat, a part of which he sells at
30% profit and the rest at 15% loss. He gains 21% on the
whole. What is the quantity sold at 30% gain and 15%
loss?
A trader has 40 kg of tea, a part of which he sells at 12%
profit and the rest at 8% loss. He gains 9% on the whole.
What is the quantity sold at 12% gain and 8% loss?