## Profit and Loss | Definitions, Formulas, Solved Problems:

**Basic Definitions and Formulas**

**Cost price (C.P.)**: This is the price at which an article is purchased.

**Selling price (S.P.)**: This is the price at which an article is sold.

**Profit or Gain:** If the selling price is more than the cost price, the difference between them is the profit incurred.

**Formula**: Profit or Gain = S.P. – C.P.

**Loss:** If the selling price is less than the cost price, the difference between them is the loss incurred.

**Formula:** Loss = Cost price (C.P.) – Selling Price (S.P.)

Profit or Loss is always calculated on the cost price.

**Marked price:** This is the price marked as the selling price on an article, also known as the listed price.

**Discount or Rebate:** This is the reduction in price offered on the market or listed price.

Below is the list of some basic formulas used in solving questions on profit and loss:

Gain % = (Gain / CP) * 100

Loss % = (Loss / CP) * 100

SP = [(100 + Gain%) / 100] * CP

SP = [(100 – Loss %) / 100]*CP

The above two formulas can be stated as,

If an article is sold at a gain of 10%, then SP = 110% of CP.

If an article is sold at a loss of 10%, then SP = 90% of CP.

CP = [100 / (100 + Gain%)] * SP

CP = [100 / (100 – Loss%)] * SP

**Profit and Loss: Solved Examples**

**Question 1:** An article is purchased for Rs. 450 and sold for Rs. 500. Find the gain percent.

**Solution:**

Gain = SP – CP = 500 – 450 = 50.

Gain% = (50/450)*100 = 100/9 %

**Question 2:** A man sold a fan for Rs. 465. Find the cost price if he incurred a loss of 7%.

**Solution:**

CP = [100 / (100 – Loss %)] * SP

Therefore, the cost price of the fan = (100/93)*465 = Rs. 500

**Question 3:** In a transaction, the profit percentage is 80% of the cost. If the cost further increases by 20% but the selling price remains the same, how much is the decrease in profit percentage?

**Solution:**

Let us assume CP = Rs. 100.

Then Profit = Rs. 80 and selling price = Rs. 180.

The cost increases by 20% → New CP = Rs. 120, SP = Rs. 180.

Profit % = 60/120 * 100 = 50%.

Therefore, Profit decreases by 30%.

**Question 4:** A man bought some toys at the rate of 10 for Rs. 40 and sold them at 8 for Rs. 35. Find his gain or loss percent.

**Solution:**

Cost price of 10 toys = Rs. 40 → CP of 1 toy = Rs. 4.

The selling price of 8 toys = Rs. 35 → SP of 1 toy = Rs. 35/8

Therefore, Gain = 35/8 – 4 = 3/8.

Gain percent = (3/8)/4 * 100 = 9.375%

**Question 5:** The cost price of 10 pens is the same as the selling price of n pens. If there is a loss of 40%, approximately what is the value of n?

**Solution:**

Let the price of each pen be Re. 1.

Then the cost price of n pens is Rs. n and

the selling price of n pens is Rs. 10.

Loss = n-10.

Loss of 40% → (loss/CP)*100 = 40

Therefore, [(n-10)/n]*100 = 40 → n = 17 (approx)

**Question 6:** A dishonest merchant sells his grocery using weights 15% less than the true weights and makes a profit of 20%. Find his total gain percentage.

**Solution:**

Let us consider 1 kg of grocery bag. Its actual weight is 85% of 1000 gm = 850 gm.

Let the cost price of each gram be Re. 1. Then the CP of each bag = Rs. 850.

SP of 1 kg of bag = 120% of the true CP

Therefore, SP = 120/100 * 1000 = Rs. 1200

Gain = 1200 – 850 = 350

Hence Gain % = 350/850 * 100 = 41.17%

**Question 7:** A man bought two bicycles for Rs. 2500 each. If he sells one at a profit of 5%, then how much should he sell the other so that he makes a profit of 20% on the whole?

**Solution:**

Before we start, it’s important to note here that it is not 15% to be added to 5% to make it a total of 20%.

Let the other profit percent be x.

Then, our equation looks like this.

105/100 * 2500 + [(100+x)/100] * 2500 = 120/100 * 5000 → x= 35.

Hence, if he makes a profit of 35% on the second, it comes to a total of 20% profit on the whole.

**Question 8:** A shopkeeper allows a discount of 10% on the marked price and still gains 17% on the whole. Find at what percent above the cost price did he mark his goods.

**Solution:**

Let the cost price be 100. Then SP = 117.

Let the marked price be x.

So, 90% of x = 117 → x = 130.

Therefore, he marked his goods 30% above the cost price.

**Question 9:** A shopkeeper offers a discount of 20% on the selling price. On a special sale day, he offers an extra 25% off coupon after the first discount. If the article was sold for Rs. 3600, find The marked price of the article and

The cost price if the shopkeeper still makes a profit of 80% on the whole after all discounts are applied.

**Solution:**

Let the marked price of the article be x.

First, a 20% discount was offered, on which another 25% discount was offered.

So, 75% of 80% of x = 3600

75/100 * 80/100 * x = 3600 → x = 6000.

So the article was marked at Rs. 6000.

Cost price of the article = [100/(100+80)]*3600 = Rs. 2000.

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