Question

The question is- A grocer purchased 200kg of rice at rs25 per kg. He sold 80kg of at a gain of 10% and 40kg at a loss of 4%. At what rate per kg should he sell the remainder to gain 8% on his total invesment??

Answer 1

Purchase cost = 200 * 25 = Rs 5,000 

Selling price of 80 kg rice - at 10% gain => 110% of price  => (110/100) * Rs 25.
So money earned by selling 80 kg rice = 80 * 110/100 * 25 = Rs 2,200

Selling price of 40 kg rice -- at a loss of 4% => 96% of price => 96/100 *Rs 25
Money earned by selling 40 kg = 40 * 96/100 * 25 = Rs 960

Remaining quantity = 200 - 40 -80 = 80 kg

Total gain required = 8%  =>
Overall money to be earned thru sales = 108/100 * cost = 108/100 * 5,000
            = Rs 5,400

Money to be earned through sale of remaining 80 kg
       = Rs 5,400 - Rs 2,200 - Rs 960 = Rs 2,240

Selling price of the remainder rice = Rs 2,240 / 80 kg = Rs 28/kg

Answer 2

Total cost price = 200×25

                          = 5000

Selling price of 80 kg rice

Gain% = 10%

           = (110/100)×25

Money earned = 11/100×8×25

                         = rs. 2,200

Selling price of 40kg rice

Loss% = 4%

          = (96/100)×25

Money earned = 96/100×40×25

                        = rs.960

Remaining quantity = 200-(40+80)

                                = 80kg

Total gain% required = 8%

Total investment = 108/100×5000

                            = rs. 5,400

Selling price of remaining 80kg

=5400-(2200-960)

= rs. 2240

= 2240/80

=28/kg

Thus,he must sell the remaining 80kg at 28/kg.

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