A shopkeeper wants to sell 100 kg of rice which he bought for Rs 10 per kg at 60% profit. Initially he sold ‘x’ kg of rice dishonestly by selling 900 grams of rice as 1 kg. Later he realizes his mistake and sells the remaining rice at 50% profit and correct measuring methods so that he earns only the profit he decided to earn earlier. Find the value of x.?

Option 2 : 36

Initial selling price = (100 + 60)/100 × CP = Rs. 16 per kg.

He sells x kg of rice at this selling price, but 900 grams is sold as 1 kg.

Amount of rice for which he charged = x/0.9 × 1 = x/0.9

Total amount for which he sold = x/0.9 × 16 = 160x/9

Remaining part of the rice is sold at 50% profit.

⇒ Selling price = (100 + 50)/50 × 10 = Rs. 15 per kg.

Remaining amount of rice = 100 – x

⇒ Total amount for which he sold = 15 × (100 – x) = 1500 – 15x

⇒ Total selling price of all 100 kg = 160x/9 + 1500 – 15x = 25x/9 + 1500

This should yield same profit that he decided to earn earlier.

Total selling price of 100kgs if he sold at the profit % he decided earlier = 100 × 10 × (100 + 60)/100 = 1600

For Profits to be same, selling price has to be same.

⇒ 1600 = 25x/9 + 1500

⇒ 100 = 25x/9