Question 130

# A merchant wants to make profit by selling food grains. Which of the following will maximize his profit?

Solution

Let the C.P. per 1000 gm of the food grain for the merchant be x.

Let us now evaluate the options one by one.

Option A says the profit is straightaway 30%.

In option B, since the weight is reduced by 15%, he will be able to cheat by selling 850 grams instead of 1000 grams.

So, his effective C.P. in this case will be 0.85x

Also, the S.P. is increased by 15% and so the S.P. will be 1.15x

Profit in this case= $$\ \frac{\ SP-CP}{CP}\cdot100$$= $$\ \frac{\ 1.15x-0.85x}{0.85x}\cdot100$$= $$\ \frac{\ 0.3x}{0.85x}\cdot100$$=35.29%.

In option C, the shopkeeper cheats by selling 700 grams instead of 1000 grams.

So, effective CP for the shopkeeper= 0.7x

The SP remains the same as original CP as nothing is mentioned about the change. So, SP=x

Profit in this case= $$\ \frac{\ SP-CP}{CP}\cdot100$$= $$\ \frac{\ x-0.7x}{0.7x}\cdot100$$= $$\ \frac{\ 0.3x}{0.7x}\cdot100$$=42.8%

In Option D, if he mixes 30% impurities, for 1000 grams of food grain, he will be able to sell 1300 grams of food grains.

So, Effective CP remains the same=x

Effective SP= 1.3x

Profit in this case= $$\ \frac{\ SP-CP}{CP}\cdot100$$= $$\ \frac{\ 1.3x-x}{x}\cdot100$$= $$\ \frac{\ 1.3x}{x}\cdot100$$=30%

We can see that the profit is maximum in the third case, and hence, Option C is correct.

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