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# How To Solve Profit And Loss Question Quickly

**How to solve Profit and Loss Questions Quickly**

Profit and Loss is the most important topic in quantitative section of all the job entrance exams. This page here on contains information about how to solve Profit and Loss questions Quickly.

### Basic Concepts on Profit and Loss

Concepts to solve Profit and loss questions:

**Cost Price –**Cost Price is the price at which an article is purchased by the buyer. It is abbreviated as C. P.**Selling Price –**Selling Price is the price at which any material or commodity is sold to known.**For ex**– Rahul is selling sugar. Here selling refers to SELLING PRICE .**Gain or Profit –**If SP is greater than CP then the seller is said to have profit or gain.

### Basic Concepts of Profit and Loss

**Use Unitary Method**: If the profit or loss is given on a single item, you can use the unitary method to find the profit or loss on multiple items quickly. For example, if the profit on one item is $5, the profit on 6 items would be 6 times $5.**Shortcut for 10%**: To calculate 10% of any amount, simply move the decimal point one place to the left. For example, 10% of $50 is $5.**Shortcut for 5%**: To calculate 5% of any amount, first find 10% using the above shortcut and then halve it. For example, 5% of $60 is (10% of $60)/2 = $6/2 = $3.**Discounts and Markups**: If the question involves discounts or markups, understand that a discount is a reduction from the selling price, and a markup is an increase over the cost price.**Reversal Method**: If the cost price and the profit percentage are given, but the selling price needs to be found, you can use the reversal method. Divide the profit percentage by 100, add 1, and then multiply it by the cost price to find the selling price. For example, if the cost price is $80 and the profit percentage is 25%, the selling price would be (1 + 0.25) x $80 = $100.

### Basic Formulas of Profit and Loss

**Profit (P):**

Profit = Selling Price (SP) – Cost Price (CP)**Loss (L):**Loss = Cost Price (CP) – Selling Price (SP)**Profit Percentage (Profit %):**Profit%=\frac{Profit}{Cost.Price}\times100**Loss Percentage (Loss %):**Loss% = \frac{Loss}{\text{ Cost Price }}\times100**Marked Price (MP) and Discount Percentage (Discount %):**Discount = \frac{\text{ Discount Precentage}}{100}\times {\text{Marked Price}}**Discount Percentage (Discount %):**Discount%=\frac{Discount}{\text{ Marked Price}}\times100

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### How to Solve Profit and Loss Questions Quickly

**Question 1.** **A man sold an article at a loss of 20%. If he has sold that article for Rs. 12 more he would have gained 10%. Find the cost price of that article :**

**Options**:

**A. Rs. 60**

**B. Rs. 40**

**C. Rs. 30**

**D. Rs. 22**

**Solution: **

Assume the cost of article is x

the person sold at 20% loss

Loss = \frac{CP – SP}{CP}

= (x−S.P)/x

= 20/100

∴ S.P = 0.8 x

If he had sold it for Rs. 12 more, then he would have gained 10%.

Gain % = \frac{SP – CP}{CP}

= \frac{0.8x + 12 – x}{x}

= \frac{10}{100}

∴12−0.2x=0.1x

∴12=0.3x

∴x=40Ans.

**Correct option: B**

**Question 2. If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage.**

**Options**:

**A. 40%**

**B. 55%**

**C. 35%**

**D. 30%**

**Solution: **Let the cost be Rs x.

After giving 25% discount it becomes 0.75x

Selling price = 0.75x which gives 25% profit… (1)

Thus, after giving 10% discount it becomes 0.90x

Selling price = 0.90x …… (2)

From (1) and (2),

0.90x will gives \frac{25 × 0.90x}{0.75x} = 30 % profit.

**Correct option: D**

**Question 3.Shopkeeper bought a product for Rs1000 per kg and is selling that at the same price. However he uses, a weighing scale that gives scale of 1kg for every 800gms. What is his profit?**

**Options**:

**A. 56% profit**

**B. 55% loss**

**C. 25% profit**

**D. None of these**

**Solution**: Gain% = \frac{True\: weight – False\: weight}{False\: weight}\times 100

= \frac{1000 – 800}{800}\times 100

= \frac{2}{8}\times 100

= 25% profit

** Correct option: C**

### How To Solve Questions based on given Percentage

**Question 4. A shopkeeper bought a watch for Rs.400 and sold it for Rs.500.What is his profit percentage?**

**Options**:

**A. 35%**

**B. 25%**

**C. 30%**

**D. 20%**

**Solution: **Cost price=400

Selling price=500

profit%= \frac{Total \: Profit}{Cost\: Price} × 100

profit=500-400=rs.100

profit%= \frac{100}{400} × 100

= \frac{100}{4}

=25%

**Correct option: B**

**Question 5. A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.55 more he would have had a profit of 40%. The cost price of the article is.**

**Options**:

**A. 125**

**B. 150.5**

**C. 112.5**

**D. None**

**Solution: **Now x is CP , sold it at a loss of 10%= \frac{90x}{100}= \frac{9x}{10}

Bought it for 20% less= \frac{80x}{100}= \frac{4x}{5}

profit 40%of \frac{4x}{5}= \frac{140}{100}× \frac{4x}{5}= \frac{56x}{50}

\frac{56x}{50}– \frac{9x}{10}=55rs

\frac{560x-450x}{500} =55rs

\frac{110x-}{500}=55rs

x= \frac{500*55}{110}

x= \frac{27500}{110}=250

X-250

**Correct option: D**

**Question 6. If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage.**

**Options**:

**A. 40%**

**B. 55%**

**C. 45%**

**D. 30%**

**Solution: **Let the cost be Rs x.

After giving 25% discount it becomes 0.75x

Selling price = 0.75x which gives 25% profit…(1)

Thus, after giving 10% discount it becomes 0.90x

Selling price = 0.90x ……(ii)

From (1) and (2),

0.90x will gives = \frac{25 * 0.90x}{0.75x}

= 30 % profit.

**Correct option: D**

**Question 7. A cow and a horse are bought for Rs 200000. The cow is sold at profit of 20% and the horse at a loss of 10%.the overall gain is Rs 4000. The cost price of cow is?**

**Options:**

**A. 36000**

**B. 80000**

**C. 54000**

**D. 45000**

**Solutions: **Let, the cost price of cow be c and that of horse be h.

Then,

c+h=200000

Selling price of Cow & Horse = \frac{6c }{5} + \frac{9h}{10}

= \frac{12c + 9h}{10}

now, \frac{12c + 9h}{10}=204000

12c+9h =2040000 …..(eq 1)

12c+12h=2400000 …..(eq 2)

3h = 360000

=> h= Rs.120000

c=200000-120000

=80000

Cost of cow = Rs. 80000

Cost of Horse=Rs. 36000

**Correct Option B**

**Question 8. ****A merchant buys 20 kg of wheat of Rs.30 per kg and 40 kg wheat at Rs.25 per kg. He mixed them and sells one third of the mixture at Rs.26 per kg. The price at which the merchant should sell the remaining mixture, So that he may earn a profit of 25 % in his whole outlay is?**

**Options:**

**A. Rs 30**

**B. Rs 36**

**C. Rs 37**

**D. Rs 40**

**Solution: **Cost price of all the wheat=(20*30)+(40*25)=1600

if he makes 25% profit then total selling

price=1600 × \frac{5}{4}=2000

total mixture of wheat is 60kg. one third of which is 20kg.

Now selling price of 20kg of wheat=20*26=520

so 40 kg of wheat = \frac{2000-520}{40}=37.

**Correct Option C**

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question no :7

Kindly join our Discord channel or all the technical or course related queries.

First solution has 1L milk in 5L solution, hence 0.2L milk/ liter of sol. 2nd sol has 0.33L milk/liter of sol. Then he take 3L of first sol and 2L of second sol. so, the final mixture has 0.2*3+0.33*2=1.26L of milk in 5L of Mixture.

Let he sold first sol in Re1 with 20% gain, means 1L milk with Re0.2 gain.

In the final mix he sold 0.26L free wich have a profit of (0.2/1)*0.26=0.052=5.2% loss

can anyone please explain this solution?

Please contact the mentors on our telegram TA prepinsta group where they will explain it thoroughly.

Do correction on “”Tips & Tricks & Shortcuts to solve type of Profit & Loss “”

In Type 3 problem ,You should write Rs60 in place of Rs.48

A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?

Explanation

(20/100-20)=25%

25% is equivalent to 10 kg

10*4=40

100/40=2.5

the original price is 2.5 kg

explain this

Hi Hemanth,

Here is your answer …

Let price of salt = x

Before reduction in price , x * y kg = 100 rs. i.e. xy = 100 or y = 100/x eq.1

After reduction of 20% in price , (80x/100) * (y +10) kg = 100 rs. i.e. (4x/5) * (y+10) = 100 eq. 2

put the value of y (from eq. 1) to eq. 2

we get x = 2.5

Hence, the original price is 2.5 .

We Hope you get it ,

All The Best.

problem 5

please explain these steps

profit 40%of 4x/5=140x/100*4x/5=56x/50

56x/50-9x/10=55rs

Hey Hemanth,

profit = (100 + profit(in %)) * cost price.

Thank you.

In question 7, how equation 2 is formed??

Hello avinash,

we hope you are doing great..

In question 7 , eq 2 is formed by multiplying 12 to c+h = 200000 (written on the 2 line of the answer).

question no 2 explaination not justified for

Thus, after giving 10% discount it becomes 0.90x

Selling price = 0.90x ……(ii)

From (1) and (2),

0.90x will gives = (25 * 0.90x)/ (0.75x)

= 30 % profit.

Hii Ashima,

The solution is right as 25/0.75x is the profit on 0.75 selling price so on 0.90 selling price it will be (0.90x * 25)/0.75x

Thank You.