# Profit and Loss – Aptitude Questions and Answers

Profit and loss are crucial topics in Quantitative Aptitude sections of various competitive exams. To succeed in these exams, candidates must have a solid understanding of the cost price (CP) and selling price (SP) formulas, as well as the different types of profit and loss questions.

Get a comprehensive guide to profit and loss aptitude questions and answers with different types of questions that candidates are likely to encounter in exams, and provide clear explanations and useful tricks to help them solve these problems with ease. By mastering the concepts and techniques mentioned in this article, candidates can enhance their problem-solving and aptitude skills and increase their chances of success in competitive exams.

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## Profit and Loss Formulas

Profit and Loss is a topic that is definitely asked in every placement exam. While the questions are not too tricky, some require deeper understanding of concepts, but most of them are based on certain well-known formulas.

## S.No | ## Name | ## Formulas |

1. | Profit | Profit = Selling Price – Cost Price |

2. | Loss | Loss = Cost Price – Selling Price |

3. | Profit Percentage | Profit% = (Profit / Cost Price) x 100% |

4. | Loss Percentage | Loss% = (Loss / Cost Price) x 100% |

5. | Selling Price | Selling Price = [(100 + Profit%) / 100] x Cost Price |

6. | Cost Price | Cost Price = [100 / (100 + Profit%)] x Selling Price |

7. | Selling Price (after discount) | Selling Price = [(100 – Loss%) / 100] x Cost Price |

8. | Cost Price (after discount) | Cost Price = [100 / (100 – Loss%)] x Selling Price |

9. | Discount | Discount = Marked Price – Selling Price |

## Sample Questions on Profit and Loss

### Q1: A person buys a pen from a wholesaler at Rs. 10 for 20 pens. He sells those pens at Rs. 10 for 15 pens. Find his profit or loss percent.

** Solution**:

CP for each pen = 10 / 20 = Rs. 0.50 SP for each pen = 10 / 15 = Rs. 2 / 3 Profit = SP – CP = Rs. (2 / 3) – 0.50 = Rs. 1 / 6 Therefore, profit percent = [ (1/6) / (0.50) ] x 100 = 33.334%

### Q2: A dealer incurs a loss of 5 % if he sells an article for Rs. 1805. What price must he sell the article so as to gain 5 % on that article?

** Solution**:

Let the cost price of the article be Rs. C => SP = CP – Loss => 1805 = C – 0.05 C => 0.95 C = 1805 => C = 1900 Therefore, to gain 5 %, SP = 1900 + (0.05 x 1900) = 1900 + 95 = Rs. 1995

### Q3: If the cost price of an article is 67 % of the selling price, what is the profit percent?

** Solution**:

Let the selling price of the article be Rs. S => Cost price of the article = 67 % of S = 0.67 S => Profit = SP – CP = 0.33 S Therefore, profit percent = (0.33 S / 0.67 S) x 100 = 49.25 %

### Q4: A shopkeeper purchased two varieties of rice, 80 KG at Rs. 13.50 per KG and 120 KG at Rs. 16 per KG. The shopkeeper being greedy, mixed the two varieties of rice and sold the mixture at a gain of 16 %. Find the per KG selling price of the mixture.

** Solution**:

We are given that the shopkeeper bought 80 Kg at Rs. 13.50 per KG and 120 KG at Rs. 16 per KG. => Total cost price = (80 x 13.50) + (120 x 16) = 1080 + 1920 = Rs. 3000 and total rice = 80 + 120 = 200 KG Now, total selling price = Total cost price + 16 % of total cost price => Total selling price = 3000 + (0.16 x 3000) = Rs. 3480 Thus, selling price per KG = 3480 / 200 = Rs. 17.40

Another method: We can do this question by allegation also.

=> (m – 13.50) / (16 – m) = 120 / 80 => m = 15, where ‘m’ is the per KG cost price of the mixture Therefore, per KG selling price of the mixture = Rs. 15 + 16% of 15 = Rs. 17.40

### Q5: A seller claims to sell at cost price but gives 750 gm for each KG. Find his gain percent.

** Solution **:

Profit percent = [ (True Value – Given Value) / Given Value ] x 100 % Here, True Value = 1 KG = 1000 gm Given Value = 750 gm Therefore, profit percent = [ (1000 – 750) / 750 ] x 100 = (250 / 750) x 100 = 33.334 %

### Q6: A man sold two watches at the same price, one at a 10 % profit and the other at a 10 % loss. Find his overall gain or loss percentage.

** Solution**:

We know that if two articles are sold at the same selling price, one at a gain of A% and one at the loss of A%, then the seller always incurs a loss of (A / 10)2. => Loss percent = (10 / 10)2 = 1 %

Long Method:

Let the selling price of each watch be Rs. 99 S => Total SP = Rs. 198 S CP of first watch = SP – Profit = Rs. 99 S- 10 % of CP = Rs. 90 S CP of second watch = SP + Loss = Rs. 99 S + 10 % of CP = Rs. 110 S => Total CP = Rs. 90 S + 110 S = Rs. 200 S => Loss = Total CP – Total SP = 200 – 198 = Rs. 2 S Therefore, loss percent = (Loss / CP) x 100 = (2 S / 200 S) x 100 % = 1 %

### Q7: A shopkeeper gives two successive discounts of 20 % and 10 % on surplus stock. Further, he also gives a 5 % extra discount on cash payments. If a person buys a shirt from the surplus stock and pays in cash, what overall discount percent will he get on the shirt?

** Solution**:

Let the marked price of the shirt be Rs. 1000 => Price after first discount = Rs. 1000 – 20 % of Rs. 1000 = Rs. 1000 – 200 = Rs. 800 => Price after second discount = Rs. 800 – 10 % of Rs. 800 = Rs. 800 – 80 = Rs. 720 => Price after cash discount = Rs. 720 – 5 % of Rs. 720 = Rs. 720 – 36 = Rs. 684 Therefore, total discount = Rs. 1000 – 684 = Rs. 316 => Overall discount percent = (316 / 1000) x 100 = 31.60 %

### Q8: A dealer wants to mark the price of an article such that by offering a 5 % discount, he is able to get 33 % profit. Find the percent of CP above which the article should be marked.

** Solution**:

Let the cost price of the article be Rs. 100 => Selling price of the article = Rs. 100 + 33% of CP = Rs. 133 Let the marked price be Rs. M => Selling price = Marked Price – Discount => 133 = M – 0.05 M => 133 = 0.95 M => M = 140 => M – CP = 140 – 100 = 40 Therefore, percent of CP above which the article should be marked = (40 / 100) x 100 = 40 %

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