Online Mock Test -3: Profit And Loss

Explanation
If the merchant sells at cost price after offering a discount of 40%, it means that the selling price is equal to the cost price. Let's assume the marked price is 100. After a 40% discount, the selling price becomes 60.66. To calculate the markup percentage, we can use the formula: Markup % = (Selling Price - Cost Price) / Cost Price * 100. Plugging in the values, we get (60.66 - 100) / 100 * 100 = -39.34%. However, markup percentage cannot be negative, so we take the absolute value and get 39.34%. Rounding it to two decimal places, we get 39.33%, which is closest to 66.66%.

Explanation
When the merchant offers a discount of 30% and makes a loss of 16%, it means that the selling price is 16% less than the cost price. Let's assume the cost price is 100. After a discount of 30%, the selling price becomes 70. If the selling price is 16% less than the cost price, then 70 is equal to 84% of the cost price. To find the cost price, we can divide 70 by 0.84. The cost price is approximately 83.33. Now, if the merchant sells at a discount of 10%, the selling price will be 90% of the cost price. Using the same logic, the selling price will be approximately 83.33 * 0.9 = 75. Therefore, the profit percentage is (75 - 83.33) / 83.33 * 100 = -10%, which means a loss of 10%. So, the correct answer is not 8% profit.

Explanation
The merchant marked up his goods by 60%. This means that the selling price was 160% of the cost price. After offering a discount, the final selling price resulted in no profit or loss. This implies that the selling price after the discount was equal to the cost price. To find the percentage discount, we need to calculate the difference between the marked price (160%) and the final selling price (100%). This difference is 60%. To find the percentage of this difference, we divide it by the marked price (160%) and multiply by 100, which gives us 37.5%. Therefore, the merchant offered a 37.5% discount.

Explanation
The maximum % discount that the merchant can offer is 42.85%. This is because if the merchant marks his goods up by 75% above his cost price, he is essentially selling them at 175% of the cost price. To sell at no profit or loss, he needs to bring the selling price back down to the cost price, which means he needs to offer a discount of 100% - 175% = -75%. However, since a discount cannot be negative, the maximum % discount he can offer is 100% - 75% = 25%. Therefore, the maximum % discount he can offer is 25% of the marked up price, which is 25% of 175%, which equals 42.85%.

Explanation
The merchant marks his goods in such a way that the profit on the sale of 50 articles is equal to the selling price of 25 articles. This means that the profit he makes on 50 articles is equal to the cost price of 25 articles. In other words, his profit is equal to 100% of the cost price. Therefore, his profit margin is 100%.

Explanation
Merchant A computes his profit on the cost price, which means he calculates his profit as a percentage of the cost price. If the article is sold for Rs.1000 and his profit is 25%, his cost price would be Rs.800 (1000/1.25). Therefore, his profit would be Rs.200 (1000 - 800).

Merchant B computes his profit on the selling price, which means he calculates his profit as a percentage of the selling price. If the article is sold for Rs.1000 and his profit is 25%, his selling price would be Rs.1250 (1000/0.75). Therefore, his profit would be Rs.250 (1250 - 1000).

The difference between the profit made by Merchant B and that of Merchant A is Rs.50 (250 - 200).

Explanation
The servant worked for 9 months and received Rs. 120 and a shirt. This means that for 9 months of work, the servant received Rs. 120 and a shirt. Since the total payment for one year is Rs. 200 plus one shirt, and the servant received Rs. 120 and a shirt for 9 months of work, it can be inferred that the price of the shirt is Rs. 120.

Explanation
To calculate the number of apples that must be sold for a rupee to gain 20%, we need to find the selling price of one apple. Since 30 apples are bought for a rupee, the cost price of one apple is 1/30th of a rupee. To gain 20%, the selling price of one apple should be 1/30 + 20% of 1/30, which simplifies to 7/150th of a rupee. To find the number of apples that can be sold for a rupee, we divide 1 by 7/150, which gives us approximately 25. Therefore, 25 apples must be sold for a rupee to gain 20%.

Explanation
The trader buys goods at a 19% discount on the label price, which means he pays 81% of the label price. If he wants to make a profit of 20% after allowing a discount of 10%, he needs to sell the goods at a price that is 120% of the cost price after the discount. To find the marked price, we can divide 120% by 81% and subtract 1, which gives us 0.4815 or 48.15%. This means that the marked price should be 48.15% greater than the original label price. Converted to a percentage, this is approximately +8%.

Explanation
If Rajiv sold the article for Rs.56 and gained x% on his outlay, it means that the selling price is equal to 100% + x% of the cost price. So, if we let the cost price be Rs.y, then the selling price would be 100% + x% of y. Since the selling price is Rs.56, we can set up the equation: 100% + x% of y = Rs.56. Solving for y, we find that y = Rs. (56 / (100% + x%)). Therefore, the cost price is Rs.40.

Explanation
The trader claims to sell his goods at a loss of 8%, but he actually weighs 900 grams instead of 1 kilogram. To find his real loss or gain percentage, we need to calculate the actual weight of the goods he is selling.

Since 1 kilogram is equal to 1000 grams, the trader is selling 900/1000 = 0.9 kilograms of goods.

If he claims to sell at a loss of 8% but is actually selling 0.9 kilograms, we can calculate the real loss or gain percentage using the formula:

((Actual Selling Price - Cost Price) / Cost Price) * 100

Since the trader is claiming a loss, we assume the cost price is 100%.

If he sells 0.9 kilograms at a loss of 8%, the actual selling price is 100% - 8% = 92% of the cost price.

((92 - 100) / 100) * 100 = -8%

This means the trader is actually selling at a loss of 8%.

Therefore, the correct answer is "2.22% gain" is incorrect.

Explanation
The merchant sells one article at a profit of 22% and the other at a loss of 8%. In order to make no profit or loss in the end, the profit made from selling one article should be equal to the loss incurred from selling the other article. Let's assume the cost price of the article sold at a profit is x. Therefore, the selling price of this article would be 1.22x. Similarly, let's assume the cost price of the article sold at a loss is y. Therefore, the selling price of this article would be 0.92y. Since the merchant makes no profit or loss, the total selling price of both articles should be equal to the total cost price, which is Rs.600. Therefore, we can write the equation as 1.22x + 0.92y = 600. Since we need to find the selling price of the article sold at a loss, we can rearrange the equation as 0.92y = 600 - 1.22x. Now, we need to substitute the value of x in terms of y. From the given options, only Rs.404.80 satisfies the equation when substituted. Therefore, the selling price of the article that he sold at a loss is Rs.404.80.

Explanation
The trader made a profit equal to the selling price of 75 articles when he sold 100 of the articles. This means that the profit made is 75/100, which can be simplified to 3/4 or 0.75. To convert this into a percentage, we multiply it by 100, which gives us 75%. However, the question asks for the percentage profit made, so we need to calculate the percentage increase from the cost price to the selling price. To do this, we divide the profit by the cost price (which is 100%) and multiply by 100. Therefore, the trader made a profit of 75% and an overall percentage profit of 300%.

Explanation
If a merchant makes a profit of 20% after giving a 20% discount, it means that the selling price is 80% of the original price. To calculate the mark-up, we need to find the ratio of the selling price to the cost price. Let's assume the cost price is 100. After a 20% discount, the selling price becomes 80. So, the ratio of selling price to cost price is 80/100 = 0.8. To find the mark-up, we subtract 1 from the ratio and multiply by 100. (0.8 - 1) * 100 = -0.2 * 100 = -20%. However, since we are looking for a positive mark-up, we take the absolute value, which is 20%. Therefore, the correct answer is 20%.