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 Alligation or Mixture :-
 ::Important Formulas ::Examples

Direct Formula / Rule 22 :

• 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 :
1. 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?
2. 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 ?
3. Answers : 1 = Rs 34,   2 = Rs 11.8

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