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A shopkeeper bought sugar and rice at Rs. 30 and Rs. 50 per kg respectively and is selling them by increasing the price by Rs. 10 per kg. He also has 5 faulty weights of 1 kg each and of equal weight. When a man bought 4 kg of rice and 5 kg of sugar from him, he made an overall profit of 28%. What is the actual weight of his 1 kg faulty weight?

A shopkeeper bought sugar and rice at Rs. 30 and Rs. 50 per kg respectively and is selling them by increasing the price by Rs. 10 per kg. He also has 5 faulty weights of 1 kg each and of equal weight. When a man bought 4 kg of rice and 5 kg of sugar from him, he made an overall profit of 28%. What is the actual weight of his 1 kg faulty weight? Correct Answer 982 g

GIVEN :

A shopkeeper bought sugar and rice at Rs. 30 and Rs. 50 per kg respectively and is selling them by increasing the price by Rs. 10 per kg.

He also has 5 faulty weights of 1 kg each and of equal weight. 

 

ASSUMPTION :

Let the actual weight of the 1 kg faulty weight be ‘x’ kg

Quantity of rice he gave the man = 4x

Quantity of sugar he gave the man = 5x

 

CALCULATION :

Cost price of the products he gave the man = 50 × 4x + 30 × 5x = 200x + 150x = 350x

Selling price of 1 kg sugar = 30 + 10 = Rs. 40

Selling price of 1 kg rice = 50 + 10 = Rs. 60

Selling price of the products he gave the man = 60 × 4 + 40 × 5 = 240 + 200 = Rs. 440

Now, profit earned = selling price - cost price = 28% of cost price

⇒ 440 - 350x = 0.28 × 350x

⇒ 440 = 98x + 350x

⇒ x = 440/448 = 0.982 kg

∴ The actual weight of 1 kg faulty weight is 982 g

 

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