Profit and Loss Aptitude Questions & Formulas with answer

(c) is the correct answer.

Let the Selling Price (SP) of each item = ₹100
For Item 1 (10% Profit):
SP = CP × (100 + Profit%) ÷ 100
100 = CP × 110 ÷ 100
CP = 100 × 100 ÷ 110
CP₁ = ₹90.91
For Item 2 (10% Loss):
SP = CP × (100 − Loss%) ÷ 100
100 = CP × 90 ÷ 100
CP = 100 × 100 ÷ 90
CP₂ = ₹111.11
Total SP = 100 + 100 = ₹200
Total CP = 90.91 + 111.11 = ₹202.02
Since Total CP > Total SP, there is a Loss
Net Loss = 202.02 − 200 = ₹2.02
Loss% = (Net Loss ÷ Total CP) × 100
Loss% = (2.02 ÷ 202.02) × 100
Loss% = 1%
Shortcut Formula:
Net Loss% = (Common%)² ÷ 100
Net Loss% = (10)² ÷ 100
Net Loss% = 100 ÷ 100
Net Loss% = 1%
The person made a net loss of 1%

(c) is the correct answer.

Item P: Cost = ₹5,400, Marked Price = ₹5,860, Profit% = ---
Item Q: Cost = ---, Profit% = 25, Marked Price = ₹10,000
Ratio of Cost of P to Cost of Q = 3:4
Step 1: Find Cost of Item Q
Cost of P ÷ Cost of Q = 3 ÷ 4
5,400 ÷ Cost of Q = 3 ÷ 4
Cost of Q = 5,400 × 4 ÷ 3
Cost of Q = ₹7,200
Step 2: Find Selling Price of Item Q
Profit% = (SP − Cost) ÷ Cost × 100
25 = (SP − 7,200) ÷ 7,200 × 100
SP − 7,200 = 25 × 7,200 ÷ 100
SP − 7,200 = 1,800
SP = 7,200 + 1,800
SP of Q = ₹9,000
Step 3: Find Discount on Item Q
Discount = Marked Price − Selling Price
Discount = 10,000 − 9,000
Discount = ₹1,000
Step 4: Find Discount as % of Marked Price
Discount% = (Discount ÷ Marked Price) × 100
Discount% = (1,000 ÷ 10,000) × 100
Discount% = 10%
The discount on item Q as a percentage of its marked price = 10% (Option C)

(c) is the correct answer.

From the graph, Revenue of Q in 2015 = ₹45 million
Revenue in 2015 = Revenue in 2014 × 1.20
45 = Revenue in 2014 × 1.20
Revenue of Q in 2014 = 45 ÷ 1.20 = ₹37.5 million
Let expenditure in 2014 = x million rupees
Profit% = (Revenue − Expenditure) ÷ Expenditure × 100
10 = (37.5 − x) ÷ x × 100
10x = 3750 − 100x
110x = 3750
x = 3750 ÷ 110
x = 34.09 ≈ 34.1 million rupees
The expenditure of company Q in 2014 = 34.1 million rupees (Option C)

(₹855) is the correct answer.

One way single person fare = ₹100
Round-trip fare for 1 person = 100 × 2 = ₹200
Total fare for 5 persons = 200 × 5 = ₹1000
Discount 1 (Round-trip discount) = 10% of 1000 = ₹100
Fare after first discount = 1000 − 100 = ₹900
Discount 2 (Group of 5 discount) = 5% of 900 = ₹45
Fare after second discount = 900 − 45 = ₹855
A group of 5 tourists purchasing round-trip tickets will be charged ₹855

(a) is the correct answer.

Selling Price per unit = ₹60
Total Cost = ₹100
Total Profit = ₹500
Total Revenue = Total Cost + Total Profit
Total Revenue = 100 + 500 = ₹600
Number of units = Total Revenue ÷ Price per unit
Number of units = 600 ÷ 60 = 10 units
New Total Cost after 30% increase = 100 × 1.30 = ₹130
To maintain same profit of ₹500:
New Total Revenue = New Total Cost + Profit
New Total Revenue = 130 + 500 = ₹630
New Price per unit = 630 ÷ 10 = ₹63
Increase in price = 63 − 60 = ₹3
Price increase% = (3 ÷ 60) × 100 = 5%
The price should be increased by 5% (Option A)