Understanding Profit & Loss problems with Examples

1 Basic Definitions

Profit and Loss is important topic in Quantative Aptitude test, lets see basic definition of Profit and Loss.

The price at which articles/ item purchased is called as Cost Price (C.P.).

The price at which articles/ item sold is called as Selling Price (S.P.).

2 Profit or Gain

If Selling Price (S.P.) is more than the Cost Price (C.P.) of article/ item then the difference between selling price and cost price is known as Profit.

Profit = Selling Price (S.P.) - Cost Price (C.P)

Formula for % Gain is as follows

% Gain

= \frac{Gain}{C.P.} \times 100

Formula can be also represented as follows

% Gain

= \frac{(S.P. - C.P.)}{C.P.} \times 100

Formula for calculating Selling Price (S.P.) when % Gain/Profit and Cost Price (C.P.) is given for article.

S.P. = \frac{(100 + % Profit)}{100} \times C.P.

Formula for calculating Cost Price (C.P.) when % Gain/Profit and Selling Price (S.P.) is given for article.

C.P. = \frac{100}{(100 + % Profit)} \times S.P.

Profit Calculator

Calculate

Selling Price

Cost Price

Profit

% Profit

3 Loss

If Selling Price (S.P.) is less than the Cost Price (C.P.) of article/ item then the difference between selling price and cost price is known as Loss.

Loss = Cost Price (C.P) - Selling Price (S.P.)

Formula for % Gain is as follows

% Loss

= \frac{Loss}{C.P.} \times 100

Formula can be also represented as follows

% Loss

= \frac{(C.P. - S.P.)}{C.P.} \times 100

Formula for calculating Selling Price (S.P.) when % Loss and Cost Price (C.P.) is given for article.

S.P. = \frac{(100 - % Loss)}{100} \times C.P.

Formula for calculating Cost Price (C.P.) when % Loss and Selling Price (S.P.) is given for article.

C.P. = \frac{100}{(100 - % Loss)} \times S.P.

Loss Calculator

Calculate

Selling Price

Cost Price

Loss

% Loss

4 Profit and Loss: Solved Examples

Question 1 Lentil is purchased for Rs. 115 and sold for Rs. 135. Find the profit percent.

Solution:

Profit = SP – CP = 135 – 115 = 20.

Profit% = (20/115)*100 = 17.39 %

Question 2 A shop sold a washing machine for Rs. 14999. Find the cost price if he incurred a loss of 5%.

Solution:

CP = [100 / (100 – Loss %)] * SP

Therefore, the cost price of the Washing Machine = (100/95)*14999 = Rs. 15788.50

Question 3 In a transaction, the profit percentage is 60% of the cost. If the cost further increases by 20% but the selling price remain the same, how much is the decrease in profit percentage?

Solution:

Let us assume CP = Rs. 100.

Then Profit = Rs. 60 and selling price = Rs. 160.

The cost increases by 20% → New CP = Rs. 120, SP = Rs. 160.

Profit % = 40/120 * 100 = 30%.

Therefore, Profit decreases by 50%.

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