Question : The price of rice is decreased by 25% and therefore a person can purchase 30 kg more rice in the same expenditure. If the expenditure is INR 5,400, then what was the original price of rice per kg?
Option 1: INR 90 per kg
Option 2: INR 60 per kg
Option 3: INR 75 per kg
Option 4: INR 50 per kg
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Correct Answer: INR 60 per kg
Solution : Given: The price of rice is decreased by 25% and therefore a person can purchase 30 kg more rice in the same expenditure. The expenditure is INR 5,400. We know the formula, Expenditure = Price × Quantity. Let $x$ and $y$ be the previous price and amount of rice purchased, respectively. $xy=0.75x\times(y+30)$ ⇒ $xy=0.75xy+22.5x$ ⇒ $0.25xy=22.5x$ ⇒ $y=90$ kg The original price of rice per kg = $\frac{5400}{90}$ = INR 60 per kg. Hence, the correct answer is INR 60 per kg.
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Question : A shopkeeper bought 20 kg of rice at Rs. 55 per kg, 25 kg at Rs. 50 per kg and 35 kg of rice at Rs. 60 per kg. He spent a sum of Rs. 150 on transportation. He mixed all three types of rice and sold all the stock at Rs. 62.56 kg. His profit percent in the entire transaction is:
Option 1: 8.8
Option 2: 12.5
Option 3: 10.5
Option 4: 9.2
Question : A dishonest shopkeeper sells mangoes at INR 30 per kg, bought at INR 20 per kg, and he is giving 800 g instead of 1 kg. The shopkeeper's actual profit percentage is:
Option 1: 75%
Option 2: 37.5%
Option 3: 50%
Option 4: 87.5%
Question : In 2001, the price of a building was 80% of its original price. In 2002, the price was 60% of its original price. By what percentage did the price decrease?
Option 1: 15%
Option 2: 20%
Option 3: 25%
Option 4: 30%
Question : Sourav purchased 30 kg of rice at the rate of Rs. 10 per kg and 35 kg at the rate of Rs. 11 per kg. He mixed the two. At what price per kg (in Rs.) should he sell the mixture to make a 30% profit in the transaction?
Option 1: 12.5
Option 2: 13
Option 3: 13.7
Option 4: 14.25
Question : The cost price of an article is decreased by 10% and then increased by 20%. If the final price is INR 540, then the original cost price is:
Option 1: INR 500
Option 2: INR 650
Option 3: INR 550
Option 4: INR 600
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