## Profit & loss for SSC CGL

**Hello Aspirants,**

The Profit and Loss topic is an important part of the SSC CGL (Staff Selection Commission Combined Graduate Level) exam syllabus. It falls under the Quantitative Aptitude section and tests a candidate’s ability to understand and solve problems related to profit, loss, and discount. Here are the key concepts and types of questions you may encounter in the Profit and Loss section of the SSC CGL exam:

- Cost Price (CP): The price at which an article is bought or manufactured is called the cost price.
- Selling Price (SP): The price at which an article is sold is called the selling price.
- Profit: When the selling price is higher than the cost price, it results in a profit. The formula to calculate profit is:Profit = Selling Price – Cost Price
- Loss: When the selling price is lower than the cost price, it results in a loss. The formula to calculate loss is:Loss = Cost Price – Selling Price
- Profit Percentage: The percentage profit earned on an item is calculated using the following formula:Profit Percentage = (Profit / Cost Price) * 100
- Loss Percentage: The percentage loss incurred on an item is calculated using the following formula:Loss Percentage = (Loss / Cost Price) * 100
- Marked Price (MP): The price at which an article is marked for sale is called the marked price.
- Discount: The reduction in the marked price to encourage sales is called a discount.
- Discount Percentage: The percentage discount offered on an item is calculated using the following formula:Discount Percentage = (Discount / Marked Price) * 100
- Discounted Price (DP): The price at which an article is sold after applying the discount is called the discounted price.
- Profit and Loss in Percentage Terms: Questions may ask you to find the profit or loss percentage when both the cost price and selling price are given.

Sample Questions:

- A shirt is bought for $40 and sold for $60. Calculate the profit percentage. Solution: Profit = $60 – $40 = $20 Profit Percentage = (20 / 40) * 100 = 50%
- A book is sold for $180, incurring a loss of 10%. Find the cost price. Solution: Loss Percentage = 10% Loss = (10/100) * CP $180 = CP – 0.10CP $180 = 0.90CP CP = $200
- A laptop is marked at $800, and a discount of 20% is offered. Calculate the discounted price. Solution: Discount Percentage = 20% Discount = (20/100) * $800 = $160 Discounted Price = $800 – $160 = $640

These are some basic concepts and sample questions related to profit and loss that you may encounter in the SSC CGL exam. It’s important to practice various types of problems to become proficient in solving them.

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** 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 %

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