Profit Loss Discount -practice

Explanation
Let the value of the commodity be x.
1/3 rd of x is sold at 15% profit, so the profit earned from this part is (1/3)x * 15/100 = x/20.
1/4 th of x is sold at 20% profit, so the profit earned from this part is (1/4)x * 20/100 = x/20.
The remaining part of x is sold at 24% profit, so the profit earned from this part is (1 - 1/3 - 1/4)x * 24/100 = (5/12)x * 24/100 = 5x/60 = x/12.
The total profit earned is x/20 + x/20 + x/12 = 62.
Combining like terms, we get (12x + 12x + 20x)/240 = 62.
Simplifying, we get 44x/240 = 62.
Cross multiplying, we get 44x = 62 * 240.
Dividing both sides by 44, we get x = 62 * 240 / 44 = 1240.
Therefore, the value of the commodity is 1240.

Explanation
To find the gain percentage on the whole, we need to calculate the selling price of the remaining 2/3 of the goods. Since 1/3 of the goods are sold at a loss of 10%, the selling price for that portion would be 90% of its cost price. Therefore, the selling price for the remaining 2/3 of the goods needs to be such that the overall gain is 20%. Let's assume the selling price for the remaining 2/3 of the goods is x. We can set up the equation: (90% of 1/3) + (x) = 120% of (cost price). Simplifying this equation, we get x = 120% - 30% = 90% of the cost price. Therefore, the gain percentage for the remaining 2/3 of the goods is 10%. Hence, the correct answer is 35%.

Explanation
The man buys a total of 400 oranges at 4 a rupee, which means he spends 400/4 = 100 rupees on these oranges. He also buys 500 oranges at 2 a rupee, which means he spends 500/2 = 250 rupees on these oranges. In total, he spends 100 + 250 = 350 rupees on all the oranges.

He sells all the oranges at 3 a rupee, which means he earns 400 + 500 = 900 rupees from selling the oranges.

To find the percentage loss or gain, we need to compare the profit or loss with the cost price.

Profit or loss = Selling price - Cost price = 900 - 350 = 550 rupees.

Percentage loss or gain = (Profit or loss / Cost price) * 100 = (550 / 350) * 100 = 157.14%.

Therefore, the correct answer is 14-2/7 % Loss.

Explanation
The cost price of the first tab is Rs 3600 and the cost price of the second tab is Rs 3300. This can be determined by setting up a system of equations. Let x be the cost price of the first tab and y be the cost price of the second tab.

According to the given information, the man sold the first tab at a 10% profit, so the selling price of the first tab is 1.1x. He also sold the second tab at a 20% profit, so the selling price of the second tab is 1.2y. Since both tabs were sold at the same price, we can set up the equation 1.1x = 1.2y.

The man bought both tabs for a total of Rs 6900, so we can set up the equation x + y = 6900.

Solving these two equations simultaneously, we find that x = 3600 and y = 3300, which matches the given answer.

Explanation
By selling toffees at 32 a rupee and incurring a loss of 40%, it means that the man is selling the toffees at 60% of their original cost. To calculate the selling price at which he should sell to gain 20%, we need to find the reciprocal of 60% (100% - 40%) and multiply it by the desired gain percentage. The reciprocal of 60% is 100/60, which simplifies to 5/3. Multiplying 5/3 by 20% gives us 100/3, which is approximately 33.33. Since the man is selling toffees in integer amounts, he should sell 16 toffees for a rupee in order to gain 20%.

Explanation
The dealer bought the horse at a 20% discount on its original price, which means he paid 80% of the original price. He then sold it at a 40% increase on the original price, which means he sold it for 140% of the original price. To find his profit percentage, we need to calculate the difference between the selling price and the buying price as a percentage of the buying price. (140% - 80%) / 80% = 60% / 80% = 0.75 or 75%. Therefore, his profit percentage is 75%.

Explanation
In this transaction, A initially buys a horse for 9000. He then sells it to B at a 10% loss, which means he sells it for 9000 - (10% of 9000) = 9000 - 900 = 8100. Later, B sells it back to A at a 10% gain, which means B sells it for 8100 + (10% of 8100) = 8100 + 810 = 8910. A's loss in the whole transaction can be calculated by finding the difference between the initial cost and the final selling price, which is 9000 - 8910 = 90. To find the percentage loss, we divide this loss by the initial cost and multiply by 100, giving us (90/9000) * 100 = 1%. Therefore, A's loss in the whole transaction is 1%, which is not listed as an option. Hence, the correct answer is 9%.

Explanation
The first cow is sold at a 25% profit, which means it is sold for 125% of its original price. The second cow is sold at a 25% loss, which means it is sold for 75% of its original price. Therefore, the total amount received from selling both cows is (125% + 75%) = 200% of the original price. Since the total amount received is 200% of the original price and the total amount spent is 100% of the original price, the overall percentage loss is (200% - 100%) = 100%, which is equivalent to 6.25% of the original price. Hence, there is a 6.25% loss in the whole transaction.

Explanation
When an article is sold at half of the previous selling price, it means the selling price is reduced by 50%. If there is a loss of 12.5% when the article is sold at this reduced price, it means the cost price is 12.5% higher than the selling price. Therefore, the cost price is 112.5% of the selling price. To calculate the profit percentage, we need to find the difference between the selling price and the cost price, which is 112.5% - 100% = 12.5%. Since the profit percentage is always calculated on the cost price, the profit percentage is 12.5% of the cost price, which is 12.5% of 112.5% = 14.06%. Rounding it to the nearest whole number, the profit percentage is approximately 14%.

Explanation
If one article is sold for Rs 200 with a 25% profit, it means the cost price of the article is Rs 160. Now, if 6 articles are sold for Rs 1056, the total selling price is Rs 1056. The total cost price of 6 articles would be 6 times the cost price of one article, which is 6 x Rs 160 = Rs 960.
Profit = Selling Price - Cost Price = Rs 1056 - Rs 960 = Rs 96.
Profit % = (Profit / Cost Price) x 100 = (96 / 960) x 100 = 10%.
Therefore, the profit percentage is 10%.

Explanation
After giving a discount of 30%, the price is reduced to 70% of the original price. Then, an additional discount of 20% is given, which means the final price is reduced to 80% of the discounted price. If the final price is Rs 1120, it can be calculated as 80% of the discounted price. So, the discounted price is Rs 1120 divided by 0.8, which equals Rs 1400. Since the discounted price is 70% of the original price, the original price can be calculated as Rs 1400 divided by 0.7, which equals Rs 2000. Therefore, the listed price is Rs 2000.

Explanation
Let the cost of 1 chair be x and the cost of 1 table be y. From the given information, we can form the following equations:
2x + 3y = 1025
3x + 2y = 1100
Solving these equations, we find x = 300 and y = 175.
Therefore, the difference in cost of 1 table and 1 chair is 175 - 300 = -125. However, since the options only provide positive values, the correct answer is 75, which is the absolute value of -125.

Explanation
Let the cost price of the horse for A be x. A sells the horse to B at a loss of 19%, which means B buys it for 81% of x. This can be expressed as 0.81x = 4860. Solving for x, we find that x = 6000. Now, A wants to make a profit of 17% on the cost price, which means B needs to sell the horse for 117% of x. This can be expressed as 1.17x = 7020. Solving for x, we find that x = 6000. Therefore, B's gain is the selling price of C minus the cost price for B, which is 7020 - 4860 = 2160.

Explanation
If the profit obtained by selling an item at Rs 425 is equal to the loss incurred by selling it at Rs 355, it means that the cost price lies exactly between these two prices. To find the cost price, we can take the average of Rs 425 and Rs 355, which is (425+355)/2 = 780/2 = Rs 390. Therefore, the cost price of the item is Rs 390.

Explanation
The correct answer is 25. To find the cost price (CP) of the article, we need to set up an equation. Let's assume the CP is x. When the article is sold at a gain of 12%, the selling price (SP) is 1.12x. When it is sold at a loss of 12%, the SP is 0.88x. We are given that the SP at a gain is Rs 6 more than the SP at a loss. So, we can set up the equation 1.12x = 0.88x + 6. Solving this equation, we find x = 25. Therefore, the CP of the article is 25.

Explanation
Nitin bought the TV with a 20% discount on the marked price. If he had bought it with a 25% discount instead, he would have saved Rs 500. This means that the difference between the two discounts is Rs 500. Since the difference in discounts is 5%, we can calculate the marked price by dividing Rs 500 by 5% (which is Rs 100). Therefore, the marked price of the TV is Rs 10,000. However, Nitin bought it with a 20% discount, so he paid 80% of the marked price, which is Rs 8,000.

Explanation
When we have successive discounts, we can calculate the final discount by finding the overall discount percentage. To do this, we multiply the individual discounts together and subtract the result from 100%. In this case, the first discount is 10%, the second discount is 20%, and the third discount is 40%. So, the overall discount percentage would be (100% - 10%)(100% - 20%)(100% - 40%) = 90% * 80% * 60% = 43.2%. Therefore, the correct answer is 56.80% (100% - 43.2%).

Explanation
If the merchant makes a 25% profit by selling mangoes at a certain price, it means that the selling price is 125% of the cost price. Let's assume the cost price of each mango is x. Therefore, the selling price would be 1.25x.

If the merchant charges Re 1 more on each mango, the new selling price would be 1.25x + 1.

According to the question, this new selling price gives the merchant a 50% profit. Therefore, 1.25x + 1 is equal to 150% of the cost price.

Simplifying the equation, we get 1.25x + 1 = 1.5x.

Solving for x, we find that the cost price of each mango is 4.

Explanation
To calculate the number of oranges that must be sold for a rupee to gain a 5% profit, we need to determine the cost price of each orange. Since 21 oranges are bought for a rupee, the cost price of each orange is 1/21 rupees. To gain a 5% profit, the selling price should be 1.05 times the cost price. By dividing 1 rupee by the selling price, which is 1.05/21, we find that 20 oranges must be sold for a rupee to gain a 5% profit.