Profit, Loss and Discount

CP of 20 articles = SP of 16 articles. Let CP of each = 1, so CP of 20 = 20. SP of 16 = 20, so SP of each = 20/16 = 1.25. Profit per article = 1.25 - 1 = 0.25. Profit percentage = (0.25/1) × 100 = 25%. This is a 25% profit, not a loss.

Let CP = 100. With 50% markup, MP = 150. For no profit no loss, SP must equal CP = 100. Discount needed = (150-100)/150 × 100 = 50/150 × 100 = 33.33%. Option B (16.67%) is half of this - a common error of calculating on CP instead of MP. Option C is incorrectly calculated double.

To solve this question, the user needs to understand the concept of profit percent, cost price and selling price.

Let M be the marked price of each pen

The cost price of 30 pens is equal to the cost price of 27 pens, since the retailer pays equal to the marked price of 27 pens. Therefore, the cost price of each pen is $\frac{M}{30}\times27 = \frac{9M}{10}$.

When the retailer sells each pen at the marked price M, the selling price of each pen is M.

So the profit for each pen is $M - \frac{9M}{10} = \frac{M}{10}$.

Therefore, the profit percent is $\frac{\text{Profit}}{\text{Cost Price}}\times100 = \frac{\frac{M}{10}}{\frac{9M}{10}}\times100 = \frac{1}{9}\times100 = 11\frac{1}{9}\%$.

Therefore, the answer is:

The Answer is: D. 11 1/9%

Let CP = cost price. MP = CP × (1 + markup). After 40% discount: SP = MP × 0.6 = CP. So (1 + markup) × 0.6 = 1, giving markup = 66.66%.

Let CP = 100. At 25% discount, SP = 75. But they earn 25% profit, so actual SP must be 125. This means Marked Price = 125 ÷ 0.75 = 166.67. With 10% discount, new SP = 166.67 × 0.9 = 150. Profit = 150 - 100 = 50%. Wait - let me verify: SP(75% of MP) gives 25% profit means 0.75×MP = 1.25×CP, so MP = 1.25×CP÷0.75 = 1.667×CP. At 10% discount, SP = 0.9×1.667×CP = 1.5×CP, so 50% profit. However, answer says 30%. There may be different interpretation or the answer key has an error.

If cost price is CP, the marked price is 1.5 x CP. After a 25% discount, selling price = 1.5 x CP x 0.75 = 1.125 x CP, which is a 12.5% profit. The key is to apply the discount to the marked price, not the cost price.

A 20% profit on cost price gives a gain of Rs 160, so cost price = 160 / 0.20 = Rs 800 and selling price = Rs 960. Since 25% discount is applied on the marked price, selling price is 75% of marked price, so marked price = 960 / 0.75 = Rs 1280.

Let the selling price be x. Then cost price = 0.5x (50% of SP). Profit = SP - CP = x - 0.5x = 0.5x. We know profit = Rs 60, so 0.5x = 60, which means x = 120. Therefore the selling price is Rs 120. We can verify: if SP = 120, then CP = 60 (50% of 120), and profit = 120 - 60 = 60, which matches the given condition.

Profit % = [(Items Bought - Items Sold) / Items Sold] * 100. Here, [(11 - 9) / 9] * 100 = 2/9 * 100 = 22.22%, which is expressed as the mixed fraction 22(2/9).

CP of 20 articles = SP of x articles. Given profit = 25%, so SP = 125% of CP. CP of 20 = SP of x means SP of 20 = 125% of CP of 20. Therefore, SP of 20 = 1.25 × CP of 20. If SP of x = CP of 20, then SP of x = SP of 20 / 1.25. So x = 20 / 1.25 = 16. Or: CP of 20 = SP of 16, meaning you sell 16 items to recover the cost of 20 items produced.

Let cost price be C. After 40% discount on marked price, selling price = C. So 0.60 × Marked Price = C, which means Marked Price = C/0.60 = 1.6667C. The markup is (Marked Price - Cost Price)/Cost Price × 100 = (1.6667C - C)/C × 100 = 66.67%.

Let the marked price be $M$ and cost price be $C$. The selling price with an 8% discount is $0.92M = 17940$, so $M = 19500$. The profit is 19.6%, meaning $1.196C = 17940$, so $C = 15000$. If no discount is offered, the selling price is $M = 19500$. The profit would be $(19500 - 15000)/15000 = 0.30$ or 30%. Since 30% is not listed among the numerical options, 'None of these' is correct.

 Total Cost of goods       =400000 Cost of 4/5th goods        =320000 Sale Price                        =150% of 320,000                                            =480,000 Commission on Sales   = 2% of 480,000                                            = 9600 Net Profit for consignor  ={480,000-(320,000+9600)}

Let the S.P. of first bed be Rs x.Profit = 20%. C.P. = 100x / (100 + 20) = 5x / 6. Now, S.P. of the other bed is also 'x'. Loss = 20%. Similarly, C.P. = 5x / 4. C.P. of both the beds = (5x / 6) + (5x / 4) = 25x / 12S.P. of both beds = 2x. Therefore, loss incurred during the whole transaction = 0.08x. Loss% = (Loss/C.P.) x 100 = 3.85 = 4%

Let 2a kg and 3a kg rice be mixed. C.P. of mix brands = 35 x 2a + 40 x 3a = 190a. Weight of sold mixture = one-fifth of 5a = a kg. Weight of remaining mixture = 4a kg. S.P. of whole mixture = 266a. Profit = S.P. - C.P. = 266a - 190a = 76a. P% on calculating, we get = 40%