Theorem:
If a person buys n kg of an item at the rate of Rs
P per kg. If he sells m kg at a profit of x%, then the rate per kg, at which he should sell the remaining
to get a profit of y% on the total deal, is given by
Rs P
=
[
1 +
ny - mx
]
(n - m)100
Example :
Jayshree purchased 150 kg of wheat at the rate of Rs
7 per kg. She sold 50 kg at a profit of 10%. At what
rate per kg should she sell the remaining to get a
profit of 20% on the total deal?
Detail Method :
Selling price of 150 kg wheat at 20% Profit
= 150 X 7 (120/100) = Rs 1260
Selling price of 50 kg wheat at 10% profit
= 50 X 7 (110/100) = Rs 385
So selling price per kg of remining 100 kg wheat
=
1260 - 385
= Rs 8.75
100
Ailigation Method :
Selling price per kg at 10% profit = Rs 7.70
Selling price per kg at 20% profit = Rs 8.40
Now, the two lots are in ratio = 1 : 2
7.7
8.4
x
1
2
=
8.4 - 7.7
=
2
x - 8.4
1
x - 8.4 =
0.7
2
x - 8.4 = 0.35
x = 8.75
Quicker Method : Here you can use direct formula :
the required answer
=
[
150 X 20 - 50 X 10
+ 1
]
X 7
(150 - 50) X 100
=
[
3000 - 500
+ 1
]
X 7
100 X 100
= 5/4 X 7 = 35/4 = Rs 8.75 per kg.
Exercise :
Sugandha purchased 160 kg of rice at the rate of Rs 25
per kg. She sold 60 kg at a profit of 20%. At what rate per
kg should she sell the remaining to get a profit of 30% on
the total deal?
Sunanda purchased 80 kg of wheat at the rate of Rs 10
per kg She sold 30 kg at a profit of 10%. At what rate per
kg should she sell the remaining to get a profit of 15% on
the total deal ?