Solved Examples on Profit and Loss | Mathematics for RRB NTPC / ASM - RRB NTPC/ASM/CA/TA PDF Download

Introduction

Profit and loss is a fundamental concept in business and economics, focusing on the financial outcomes of buying and selling goods or services. It involves determining the difference between the cost price (CP) and selling price (SP), which helps in calculating whether a transaction results in profit or loss.  This topic holds significant importance as it tests a candidate's ability to apply basic mathematical principles to real-life business situations. The ability to quickly and accurately solve profit and loss problems is essential for various competitive exams. Mastery of this concept is crucial for scoring well in these exams, as it is frequently included in the quantitative reasoning section.

 Important Terms

•  Cost price (CP): The price at which an article is purchased
•  Sale Price (SP): The price at which an article is sold.
•  Overhead charges: Apart from the actual cost price, if some charges have to be paid are called overhead charges. Such charges are freight, rent, salary of employees etc.
•  Profit (If SP > CP): If sale price of a commodity is more than the cost price, some profit is earned.
•  Loss (If SP < CP): When an article is sold at a price less than the cost price, loss is incurred.

 IMPORTANT FORMULAE

1) Profit = Sale price – cost price

P = SP – CP

 2) Loss = Cost price – Sale price

L = CP – SP

 3) Profit % = (Profit / Cost Price) x 100

= (P / CP) x 100

 4) Loss % = (Loss / cost price) x 100

= (L / CP) x 100

5) Selling Price when Gain % is Given

SP = CP × (1 + G/100)

 6) Selling Price when Loss % is Given

SP = CP × (1 - L/100)

7) Cost Price when Gain % is Given

CP = SP / (1 + G/100)

 8) Cost Price when Loss % is Given

CP = SP / (1 - L/100)

Note:

•  Profit or Loss is always on the cost price
• If an article is sold at a certain gain (say 15%) then SP = 115 % of CP
•  If an article is sold at a certain loss (say 15%)
  Then SP = 85% of CP

 Solved Examples

Example: 1 :A person buys an article for Rs. 50 and sells it for Rs. 75. What will be his gain percent?

Solution: CP = Rs. 50     SP = Rs. 75

Gain = 75 – 50 =Rs. 25

We know that gain % = (gain /cp) x 100

= (25 / 50) x 100 = 50%

 Example 2: A person buys an umbrella for Rs. 450 and sells it for Rs. 350/-. Find his loss %.

Solution: CP = Rs. 450               SP: Rs. 350

Loss = 450 – 350 =Rs. 100.

Loss percent = (Loss / CP) x 100

= (100 / 450) x 100 = 200/9 % = 

Example 3: Find the sale price if CP is Rs. 160 and gain is 20%.

Solutions: SP = 120% of CP

= (120 / 100) x 160 = Rs. 192

Example 4: Find sale price when CP is Rs. 160 and loss is 20%.

Solution: SP = 80% of CP

Or SP = (160 x 80) / 100 = Rs. 128

Example 5: Find CP when SP Rs. 64 and loss is 20%

Solution: CP = 

Example 6: Find CP when SP = 192 and profit is 20%

Solutions: CP =

Example 7: A chair is bought for Rs. 150 and sold at a gain of 8%. Find the selling price.

Solutions: SP = 

Example 8: A bicycle is bought for Rs. 1500 and sold at a loss of 6%. Find the selling price.

Solutions: CP = 1500                 Loss = 6%

=1410

Example 9: A table is sold for Rs. 1440 and there is a loss of 10%. At what price should it be sold to gain 10%.

Solutions: SP = Rs. 1440                        Loss = 10%

So CP = 

To find SP to gain 10%

CP = Rs. 1600    profit = 10%

SP = 

Example 10: Ravi lost 20% by selling a watch at Rs. 1536. What will be his gain percent if he sells if for Rs. 2040.

Solution: SP = Rs. 1536             Loss = 20%

CP = 

Now SP = Rs 2040, CP = 1920, gain = 2040 – 1920 = Rs 120

Gain percent =  

Example 11: A shopkeeper sells an article at a profit of 20%. If he had bought it at 20% less and sold for Rs. 10 less, he would have gained 25%. Find the cost price of the article.

Solution: 

Let the actual cost price be Rs. 100x

So, actual selling price = 100x × 120%

⇒ Rs. 120x

Now,

If he had bought it at 20% less than the actual then its cost price = 100x × 80%

⇒ Rs. 80x

Now, new selling price = 80x × 125%

⇒ 100x

According to the question,

120x - 100x = 10

⇒ 20x = 10

⇒ x = 1/2

So, actual cost price = 100 × (1/2)

⇒ Rs. 50

∴ The Cost Price of the article is Rs. 50.

  Example 12: A person sells apples at 10 for a rupee and gains 20%. How many apples did he buy for a rupee.

Solution: In questions where some quantity of some article is bought or sold, profit or loss is on the quantity sold

Quantity sold is 10 apples

Profit = 20%

Profit on 10 apple is 20%

So profit = 

It means he has saved 2 apples after selling 10. So he bought 12 for a rupee.

Example 13: A shopkeeper mixes 160 kg of rice at Rs. 27 per kg with 240 kg of rice at Rs. 32 per kg and sells the mixture to gain 20%. What is the sale rate of the mixture.

Solutions: Cost of 160 kg of rice @ Rs. 27 per kg.

= 160 x 27 = Rs. 4320

Cost of Rs. 240 kg of rice @ Rs. 32 per kg = 240 x 32 = 7680

Total = 7680 + 4320 = 12000

Now CP = Rs. 12000

Gain = 20%

So sale price kg =  Rs. 36 per kg

Example 14: A man buys certain no. of oranges at the rate of 3 per rupee and the same number at 4 per rupee. He mixes then together and sells at 7 for two rupees. Find his gain or loss%.

Solution: LCM of 3 and 4 is = 12

Let us suppose he purchases

12 oranges at the rate of 3 a rupee. Money spent = Rs. 4

and 12 oranges at the rate of 4 a rupee = money spent = Rs. 3

so total oranges purchased = 24

and CP = Rs. 7

now he sells 24 oranges at the rate of 7 for Rs. 2

SP = 

Loss = CP – SP = 7 -  

% loss = 

Technique to solve problems in a fast way 

If a person sells two articles, one at a loss of x % and another at a gain of x%. then there is always a loss to the seller and the loss is equal to 

Example 15: A man sells two horses for Rs. 4000 each. On one of the horses he loses 20% while on the other he gains 20%. Find his gain / loss percent in the whole transaction.

Solutions: Loss = 

Example 16: The profit on selling an article for Rs. 1196 is equal to the loss on selling the same article for Rs. 1056. The cost price of the article is:

1) 1143                                     2) 1134

3) 1156                                     4) 1126

5) None of these

Solutions: Since gain and loss on selling the same article is equal, the cost price must lie at the middle of two sale prices.

On CP =  = Rs. 1126

Example 17: On selling an article for Rs. 264 a man loses 4%. He should sell the article for how much so that his gain is 12%.

Solution: SP is given to be = Rs. 264

Loss = 4%

So CP = 

Now the gain he wants is 12%

So the SP =  

Example 18: If the selling price of 10 pens is the same as the cost price of 8 pens. Find the gain or loss percent.

Solution: 

Consider C.P of 8 pens = S.P of 10 pens =₹100

C.P of 1 pen =100.8=₹12.50

S.P of 1 pen =100/10=₹10

Loss = C.P – S.P

Substituting the values

=12.50–10

=₹2.50

Loss percent =(loss×100)/C.P

Substituting the values

=(2.50×100)/12.50

Multiplying both numerator and denominator by 100×100

=(250×100×100)/(1250×100)

=20%

Example 19: On selling 100 mangoes, a person gains the SP of 20 mangoes. Find his gain percent.

Solution: Let the SP of 100 mangoes be Rs. 100

He saves the SP of 20 mangoes which is equal to Rs. 20

So gain = Rs. 20

CP = Rs. 100 – Rs. 20 = Rs. 80

Gain % = 20/80 x 100 = 25%

Example 20: On selling a shaving machine for Rs. 1530, the loss is 10%. What will be the gain percent if the machine is sold for Rs. 1819.

Solutions: 1^st SP = Rs. 1530

Loss = 10%

Now 2^nd SP = Rs. 1819

Gain = Rs. 1819 – Rs. 1700 = s. 119

Example 21: A trader allows a discount of 15% of the marked price on his article. How much above the cost price should he mark the price to gain 19%.

Solution: let the marked price be Rs. 100.

Discount = 15%

SP = 100 – 15= 85

He wants to make a profit of 19%

So his CP should be 

If the CP is 8500/119 he should mark Rs. 100

If the CP is 1 he should mark Rs. 100 x (119 / 8500)

If the CP is 100 he should mark Rs. =

= 140so it 40 more than CP which 100

He should mark the price 40% more than the CP.

Example 22: I purchased an item for Rs. 8200 and sold it at a gain of 25%. From the sale price of the item I purchased another item and sold it at a loss of 20%. What will be the overall Gain or loss.

Solutions: CP = Rs. 8200

Gain = 25%

Again CP = 10250

Loss % = 20%

So there will not be any loss or gain.

Example 23: The cost price of an item is two third of its selling price. What is the gain / loss percent?

Solution:  let CP = Rs. 100

Then SP = 

Gain = 

Gain % = = 50%

Example 24: Apples are bought at 6 for Rs. 5 and sold at 8 for Rs. 11. Find the gain or loss per cent.

Solution: Let the no. of apples purchased and sold be 24 (LCM of 6 and 8)

CP of 24 apples = Rs. 20

SP of 24 apples = Rs. 33

Gain = Rs. 33 – Rs. 20 = Rs. 13

So gain % = 

 
Example 25: Find a single discount equivalent to three successive discounts of 10%, 20% and 40%.

Solution: On Rs. 100, 10% discount is given so SP = 100 – 10 = 90

20% discount on Rs. 90 = 

The balance amount is 90 – 18 = 72

40% of discount on Rs 72 = 

Balance amount is 72 -  

Total discount = 100 -  = 56.8%