**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

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.