Profit AND Loss Questions FOR Bank Exams with Detailed Solutions

Information Given in the Question:
First person buys at ₹1000.
Sells at 20% profit.
Second person sells at 10% loss.
Need to find overall profit or loss % compared to original cost price (Rs 1000).
Concept/Formula Used in the Question:
Selling Price (SP) = Cost Price (CP) × (1 ± Profit/Loss%)
Overall Profit or Loss = Final SP - Original CP
Percentage Profit or Loss = $$\left( \dfrac{\text{Difference}}{\text{Original CP}} \right) \times 100$$​
Detailed Explanation:
First person bought at Rs 1000
Sells at 20% profit = SP = 1000 × 1.20 = Rs 1200
Second person bought at Rs 1200
Sells at 10% loss = SP = 1200 × 0.90 = Rs 1080
Final Selling Price = Rs 1080
Original Cost Price = Rs 1000
Profit = 1080 - 1000 = Rs 80
Profit % = $$\frac{80}{1000}$$​ × 100 = 8%
Short Exam Hall Approach:
Rs 1000 → +20% → ₹1200
Rs 1200 → -10% → ₹1080
Compare final SP Rs 1080 with original CP Rs 1000
Profit = Rs 80 = 8%

Information Given:

Cost price of watch = Rs. 750

Cost price of bag = Rs. 840

Watch sold at 20% profit

Bag sold at 15% loss

Concept/Formula Used:

Profit/Loss = Selling Price – Cost Price

Profit% = (Profit / Cost Price) × 100

Selling Price (SP) at profit = CP × (1 + Profit%)

Selling Price (SP) at loss = CP × (1 – Loss%)

Overall profit/loss = Total SP – Total CP

Explanation:

SP of watch = 750 × 1.20 = Rs. 900

SP of bag = 840 × 0.85 = Rs. 714

Total cost price = 750 + 840 = Rs. 1590

Total selling price = 900 + 714 = Rs. 1614

Overall profit = 1614 – 1590 = Rs. 24

Information Given:
Selling price (actual) = Rs. 800
The article was sold for Rs. 60 more.
This new selling price is 25% more than the cost price.
Formulas Used:
Profit = Selling Price - Cost Price
$$\text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100$$​
Basic Explanation:
We are told that if the article were sold for Rs. 860, the selling price would be 25% more than the cost price.
Let the cost price be C.
860 = C + 0.25C
C = $$\frac{860}{1.25}$$​
C = 688
Profit = 800 - 688 = 112
Profit Percentage = $$\frac{112}{688} \times 100$$​ = 16.2%

Information Given:

Cost price = Rs. 2X + 500

Marked price = Rs. 2X + 1300

Profit = Rs. 2X

Discount = Rs. 2X – 200

Formula Used:

Discount = Marked Price - Selling Price

Profit = Selling Price - Cost Price

Explanation:

ATQ, 2X = Selling Price – (2X + 500)

Selling Price = 2X + 2X + 500 = 4X + 500 Rs.

Also, 2X - 200 = (2X + 1300) - (4X + 500)

2X - 200 = 2X + 1300 - 4X - 500

2X - 200 = -2X + 800

2X + 2X = 800 + 200

4X = 1000

X = 250

So, cost price of the article = 2×250+500 = 1000 Rs.

Exam Hall Approach

Information Given:

Marked Price (MP) = ₹1800

Two successive discounts: first x%, then 25%

Selling Price (SP) after both discounts = ₹1080

Profit on selling the article = x%

Find the Cost Price (CP)

Concept/Formula Used:

Successive discounts: SP = MP × (1 − x/100) × (1 − 25/100)

Profit% relation: SP = CP × (1 + x/100)

Explanation:

$$\text{ATQ, } 1080 = 1800 \times \frac{75}{100} \times \left( \frac{100 - x}{100} \right)$$ 

$$1080 = \frac{27}{2} (100 - x)$$ 

80= (100 - x)

x= 20

$$\text{So, required amount} = 1080 \times \frac{100}{120} = \text{Rs. } 900$$

Information Given:
Selling price with 25% loss = Rs. 600
In the second case:
Marked price = 25% above cost price
Profit = Rs. 150
Formulas Used:
Loss% =$$\left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100$$​
Marked Price (MP) = CP + % Markup
Selling Price = Cost Price +Profit
Basic Explanation:
Cost price = $$\frac{600}{75} \times 100$$ = Rs 800
Marked Price = 800 + 25% of 800 = 800+200 = Rs 1000
New Selling Price = 800 + 150 = Rs 950

Given:
Cost price of article A = Cost price of B - 150
Articles A and B marked up by 20% & 50% above the cost price
marked price of article B : A = 25:14
Explanation:
Let the cost price of A be Rs.x - 150
Cost price of B be Rs. x
ATQ,

10(x-150) = 7x
10x – 1500 = 7x
3x = 1500
500 = x

Information Given:
Cost price (CP) of white rice = Rs. 90/kg
CP of brown rice = Rs. 144/kg
Selling price (SP) of mixture = Rs. 168/kg
Profit on mixture = 40%
Asked: Ratio of white rice : brown rice
Concept/Formula Used:

Alligation rule:
Cheaper : Dearer = (Dearer - Mean price) : (Mean price - Cheaper)
Explanation:
CP of mixture = 168× (100/(100+40))
= 168× (100/140) = 120 Rs.
By Apply alligation between Rs. 90 and Rs. 144 to get mean 120:
Cheaper : Dearer = (144 - 120) : (120 - 90) = 24 : 30 = 4 : 5

​Given:

Discount given = Rs 960 + profit earned

Selling Price = Rs. 1920

Marked up percentage = 100%

Formula Used:

Profit =Selling Price - Cost Price
$$\text{Selling price} = \text{cost price} \times \frac{100 + \text{profit}\%}{100}\\\text{Selling price} = \text{marked price} \times \frac{100 - \text{Discount}\%}{100}$$

Explanation:

Let cost price of the article be Rs.100x

So, marked price of the article = $$100x \times \frac{200}{100} = Rs.200x$$

Atq,

​$$(200x-1920)-(1920-100x)=960 \\300x = 960 + 3840 \\x = 16 \\Required \ Profit = \frac{1920-100 \times 16}{100 \times 16} \times 100 = 20 \%$$

Exam Hall Method: 

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