

Direct Formula / Rule 10 :
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, 10x250 +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 :
Ratio of quantities sold at 10% profit and 5% loss
= 12 : 3 = 4 : 1
Therefore, the quantity sold at 10% profit
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 
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?
Answers :
1 = 72 kg, 18 kg, 2 = 36 kg, 9 kg, 3 = 34 kg, 6 kg



