Our this post is in continuation with Profit and Loss – Concepts and Solved Examples where we have discussed the concepts and type of questions asked in various exams.

Terms used are as follows:**CP** = cost price, the price at which things are bought**SP** = selling price, the price at which things are sold at a certain profit or loss**P** = profit, profit occurs when SP > CP and it equals to (SP – CP). Profit is also called gain.**L** = loss, loss occurs when SP < CP and it equals to (CP – SP)

In this post we will solve some more problems on profit and loss. So, lets dive into that.

## Basic problems

**Question**: A person buys a radio for ₹1030 and he spent ₹50 on its repairs. If he sold it for ₹1200, find the profit percentage.

(a) 10\displaystyle\frac{1}{3}\%

(b) 11\displaystyle\frac{1}{9}\%

(c) 12\displaystyle\frac{1}{2}\%

(d) Data insufficient

**Ans**: (b) 11\displaystyle\frac{1}{9}\%

**Explanation**:

Total CP = 1030 + 50 = ₹1080

SP = ₹1200

So, profit = 1200 – 1080 = ₹120

Profit percentage = \displaystyle\frac{120}{1080}\times 100 = 11\displaystyle\frac{1}{9}\%

**Question**: By selling an article at ₹285, a man loses 5%. For how much should he sell to gain 5%?

(a) ₹ 315

(b) ₹ 308

(c) ₹ 305

(d) ₹ 302

**Ans**: (a) ₹ 315

**Explanation**:

95% = 285

105% = \displaystyle\frac{285}{95}\times 105 = 315

**Question**: By selling 12 apples for a rupee, a man loses 20%. How many for a rupee should he sell to gain 20%?

(a) 8

(b) 9

(c) 10

(d) 11

**Ans**: (a) 8

**Explanation**:

SP os 12 apples = Rs. 1

So, SP of 1 apple = Rs. \displaystyle\frac{1}{12}

Now, 80% = \displaystyle\frac{1}{12}

∴ 120% = \displaystyle\frac{1}{12}\times \displaystyle\frac{120}{80} = \displaystyle\frac{1}{8}

SP is Rs. \displaystyle\frac{1}{8} per apple, so 8 apples should be sold for a rupee.

**Question**: An article is sold for ₹880 at a profit of 10%. What would have been the loss percent had it been sold for ₹780?

(a) 1.5%

(b) 2.5%

(c) 3.5%

(d) 4.5%

**Ans**: (b) 2.5%

**Explanation**:

SP = ₹ 880 at P=10%

∴ CP = \displaystyle\frac{880}{110}\times 100 = 800

New SP = 780

So, L% = \displaystyle\frac{20}{800}\times 100 = 2.5%

**Question**: A man sold an article at a loss of 20%. If he sells the article for ₹45 more, he would have got a profit of 10%. The cost price of the article is

(a) ₹150

(b) ₹140

(c) ₹120

(d) ₹100

**Ans**: (a) ₹150

**Explanation**:

30% = 45

100% = 150

**Question**: A sold an article to B at a profit of 10% B sells it to C at a loss of 10%. If C paid ₹4158, how much money was paid by A?

(a) ₹4200

(b) ₹4400

(c) ₹4560

(d) ₹4800

**Ans**: (a) ₹4200

**Expatiation**:

Let money paid by A was x

x\times \displaystyle\frac{110}{100}\times \displaystyle\frac{90}{100} = 4158

⇒ x = \displaystyle\frac{4258\times 100\times 100}{110\times 90} = 4200

**Aliter**:

Applying ab method

(10, -10) → -1%

99% = 4158

100% = \displaystyle\frac{4158}{99}\times 100 = 4200

**Question**: The ratio of the cost price and selling price of an article is 20 : 21. What is the profit percent on it?

(a) 4%

(b) 3%

(c) 5%

(d) 8%

**Ans**: (c) 5%

**Explanation**:

Let, CP = 20 and SP = 21

So, P = SP – CP = 21 – 20 = 1

P% = \displaystyle\frac{1}{20}\times 100 = 5%

## Same CP

**Question**: A man buys two cows for ₹5000 each. One is sold at a profit of 10% and other he sold at a loss of 5%. Find his profit or loss percent in the whole transaction?

(a) 2.5% profit

(b) 3% profit

(c) 2.5% loss

(d) No profit, no loss

**Ans**: (a) 2.5% profit

**Explanation**:

\displaystyle\frac{10-5}{2} = \displaystyle\frac{5}{2} = 2.5

**Question**: A man buys two articles for Rs.1800 each. He gained 10% on the first and lost 10 % on the second. Find his overall profit or loss percent in the transaction

(a) 2% profit

(b) 2% loss

(c) 2.5% loss

(d) No profit, no loss

**Ans**: (d) No profit, no loss

**Explanation**:

\displaystyle\frac{10-10}{2} = 0

**Question**: A person sells 5 cows 1^{st} at a profit of 6%, 2^{nd} at 2% loss, 3^{rd} sold on 12% profit, 4^{th} on 8% profit, what he sold 5^{th} cow to gain overall 10% profit?

(a) 26%

(b) 24%

(c) 28%

(d) 30%

**Ans**: (a) 26%

**Explanation**:

Assuming all the cows of same CP (cost price)

Net profit = average of all P and L%

Let profit in 5^{th} cow is x%

\displaystyle\frac{6-2+12+8+x}{5} = 10

⇒ 24 + x = 50

⇒ x = 26

## Same SP

**Question**: A man sells two articles for Rs.2400 each. He gained 20% on the first and losses 20% on the second. Find his overall profit or loss percent in the transaction

(a) 4% loss

(b) 4% profit

(c) 6% loss

(d) 6% profit

**Ans**: (a) 4% loss

**Explanation**: Loss % = \left(\displaystyle\frac{20}{10}\right)^2 = 2^{2} = 4

## Profit/Loss on SP

**Question**: A salesman by mistake calculates profit percentage of an articles on its selling price and says that it is 25%. What is the actual profit percentage?

(a) 33 \displaystyle\frac{1}{3}\%

(b) 33 \displaystyle\frac{1}{2}\%

(c) 33 \displaystyle\frac{2}{3}\%

(d) Data insufficient

**Ans**: (a) 33 \displaystyle\frac{1}{3}\%

**Explanation**:

Let, SP = 100

∴ P = 25

So, CP = 100 – 25 = 75

Actual Profit = \displaystyle\frac{\text{P}}{\text{CP}}\times 100

\qquad\qquad = \displaystyle\frac{25}{75}\times 100

\qquad\qquad = 33 \displaystyle\frac{1}{3}\%

## Part Selling

**Question**: Some articles are purchased for Rs. 3600. One third of them are sold at a profit of 10%. At what profit percent should the remaining articles be sold to obtain a profit percent of 15% on the whole transaction?

(a) 17.5%

(b) 17.25%

(c) 17.45%

(d) 17.65%

**Ans**: (a) 17.5%

**Explanation**:

\displaystyle\frac{1}{3}\times 10 + \displaystyle\frac{2}{3}\times \text{x} = 15

⇒ 10 +2x = 45

⇒ x = 17.5

## CP = P%

**Question**: An article was sold for Rs.75. If the percentage profit was numerically equal to the cost price, the cost price of the article is

(a) Rs. 25

(b) Rs. 50

(c) Rs. 75

(d) Rs. 100

**Ans**: (b) Rs. 50

## #Quantity – Price Type

**Question**: A man buys 12 articles for Rs.100 and sells 10 articles for Rs.120. find his profit percent

(a) 44%

(b) 48%

(c) 52%

(d) Data insufficient

**Ans**: (a) 44%

**Explanation**:

P% = \displaystyle\frac{440}{1000}\times 100 = 44%

**Question**: By selling 20 articles for a rupee a man loses 10%. How many for a rupee did he buy?

(a) 16

(b) 18

(c) 14

(d) 12

**Ans**: (b) 18

**Explanation**:

SP = Rs. \displaystyle\frac{1}{20} per article

So, at 10% loss, CP = Rs. \displaystyle\frac{1}{20\times 0.8} = Rs. \displaystyle\frac{1}{18} per article

This implies 18 articles were bought at Rs 1

**Aliter**:

10% of 20 = 2

For every 20 articles sold, loss is 2 articles.

So, he bought 18 articles a rupee

**Question**: By selling 5 articles for 1 rupee, a man loses 20%. If he sells 3 articles per rupee, what will be the profit percentage?

(a) 33 \displaystyle\frac{1}{3}\%

(b) 33 \displaystyle\frac{1}{2}\%

(c) 33 \displaystyle\frac{2}{3}\%

(d) Data insufficient

**Ans**: (a) 33 \displaystyle\frac{1}{3}\%

**Explanation**:

20% of 5 = 1

He buys (5-1) = 4 articles for a rupee

P% = \displaystyle\frac{1}{3}\times 100 = 33 \displaystyle\frac{1}{3}\%

## CP of a article = SP of b article type

**Question**: If the cost price of 15 articles be equal to the selling price of 20 articles, then find the loss% in the transaction

(a) 16%

(b) 20%

(c) 25%

(d) 26%

**Ans**: (c) 25%

**Explanation**:

15CP = 20SP

⇒ \displaystyle\frac{\text{CP}}{\text{SP}} = \displaystyle\frac{20}{15} = \displaystyle\frac{4}{3}

⇒ L% = \displaystyle\frac{1}{4}\times 100 = 25%

**Aliter**:

SP = 15, CP = 20

L% = \displaystyle\frac{5}{20}\times 100 = 25%

**Question**: If the cost price of 12 articles be equal to the selling price of 10 articles, then find the profit % in the transaction

(a) 15%

(b) 20%

(c) 25%

(d) Data insufficient

**Ans**: (b) 20%

**Explanation**:

12CP = 10SP

⇒ \displaystyle\frac{\text{CP}}{\text{SP}} = \displaystyle\frac{10}{12} = \displaystyle\frac{5}{6}

⇒ P% = \displaystyle\frac{1}{5}\times 100 = 20%

## Dishonest Dealers and Faulty Weights

We have a dedicated post on this topic. Kindly visit Dishonest Dealers and Faulty Weights for concepts and practicing problems on this topic.

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