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A shopkeeper cheats by 10% (by weight) while buying the rice. He marked up the price of rice by 25% above its cost price and offers 10% discount. If he cheats his customer by 200 grams (measure 800 grams while selling 1 kg), then what is the actual profit percent earned by the shopkeeper?

A shopkeeper cheats by 10% (by weight) while buying the rice. He marked up the price of rice by 25% above its cost price and offers 10% discount. If he cheats his customer by 200 grams (measure 800 grams while selling 1 kg), then what is the actual profit percent earned by the shopkeeper? Correct Answer 54.7%

GIVEN:

A shopkeeper cheats by 10% (by weight) while buying the rice. He marked up the price of rice by 25% above its cost price and offers 10% discount.

He also cheats his customer by 200 grams (measure 800 grams while selling 1 kg).

CONCEPT:

If the shopkeeper cheats by x% while buying ‘a’ number of items that means he is taking x% more for the price of ‘a’ items.

If the shopkeeper cheats by y% while selling ‘b’ number of items that means he is giving y% less for the price of ‘b’ items.

FORMULA USED:

Profit percentage = × 100

CALCULATION:

Suppose the cost price of 1 kg ( = 1000 gm) rice = 100x

Due to cheating by 10% (by weight) while buying, the shopkeeper bought 1100 gm at the rate of 1000 gm.

⇒ Actual cost price of 1 kg rice = 100x × 1000/1100 = Rs. 1000x/11

Now,

Marked price of 1 kg rice = 125% of 100x = Rs. 125x

After 10% discount:

Selling price of 1 kg rice = 90% of 125x = Rs. 112.5x

Since, the seller cheated his customer by 200 grams, that means he gave 800 gm rice for Rs. 112.5x.

⇒ Actual selling price of 1 kg rice = 112.5x × 10/8 = Rs. 1125x/8

Profit amount = 1125x/8 – 1000x/11 = Rs. 4375x/88

∴ Profit percentage = × 100 = 54.6875% or 54.7%

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