Profit and Loss — Basic Examples

Definitions:

Term	Meaning
Cost Price (CP)	The price at which an article is bought.
Selling Price (SP)	The price at which an article is sold.
Profit	SP − CP (when SP > CP).
Loss	CP − SP (when SP < CP).
Profit%	(Profit / CP) × 100.
Loss%	(Loss / CP) × 100.

Examples

Example 1 — Simple profit

CP = $100$, SP = $120$

Profit = $120 - 100 = 20$

Profit% = $\dfrac{20}{100}\times 100 = 20\%$.

Example 2 — Simple loss

CP = $150$, SP = $120$

Loss = $150 - 120 = 30$

Loss% = $\dfrac{30}{150}\times 100 = 20\%$.

Example 3 — Find SP from CP and profit%

Marked Price (MP) = Rs. 450

Discount = 10%

→ Discount Amount = $( \dfrac{10}{100} \times 450 = Rs. 45 )$

→ Selling Price (SP) = Rs. 450 − Rs. 45 = Rs. 405

Example 4 — Find SP from CP and profit%

Given CP = $200$, profit% = $15\%$.

Profit = $200\times\dfrac{15}{100}=30$

SP = $200+30=230$

Example 5 — Find CP from SP and profit%

Given SP = $460$, profit% = $15\%$.

Let CP = $x$.

Profit = $x\times\dfrac{15}{100} = \dfrac{15x}{100}$.

So SP = CP + Profit = $x + \dfrac{15x}{100} = \dfrac{115x}{100} = \dfrac{23x}{20}$.

Therefore $\dfrac{23x}{20}=460 \Rightarrow x = 460\times\dfrac{20}{23} = 400$.

So CP = Rs. $400$.

Profit = $460-400=60$ (which is $15\%$ of 400).

Example 6 — Find SP from CP and loss%

Given CP = $80$, loss% = $25\%$.

Loss = $80\times\dfrac{25}{100}=20$

SP = $80-20=60$

Example 7 — Find profit% from CP and SP

Given CP = $250$, SP = $300$.

Profit = $50$

Profit% = $\dfrac{50}{250}\times 100 = 20\%$.

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Q1. Bimal bought a basket for Rs. 300 and sold it for Rs. 390. Calculate the Profit percentage (p%)

Reveal solution

• CP = Rs. 300
• SP = Rs. 390
• Profit = SP − CP = Rs. 90
• Profit Percent = $( \dfrac{90}{300} \times 100\% = 30\% )$

So, Bimal made a 30% profit.

Q2. Deepak bought 12 copies for Rs. 360 and sold 2 copies for Rs. 62. Calculate the profit per copy.

Reveal solution

• CP per copy = Rs. 360 ÷ 12 = Rs. 30
• SP per copy = Rs. 62 ÷ 2 = Rs. 31
• Profit per copy = Rs. 1

So, Deepak made Re. 1 profit per copy.

Q3. A photocopy machine was sold at Rs. 60,000 with a 20% loss. Find SP for 12% profit.

Reveal solution

• Let CP = Rs. x

• Loss = 20% of x = $( \dfrac{x}{5} )$

  So, $SP = x - \dfrac{x}{5}$

$\Rightarrow \dfrac{4x}{5} = 60000$

$\Rightarrow x = 75000$

Desired Profit = 12% of CP = Rs. 9,000

New SP = Rs. 75,000 + Rs. 9,000 = Rs. 84,000