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?