UNIT 10 • INTEREST & FINANCE

Percentage Calculator
Change, Profit & Loss, Discount

A percentage is a number out of 100: $x\% \text{ of } y = \frac{x}{100} \times y$ . The same idea gives percent change, profit and loss (on cost price), discounts (on marked price), and markup and margin.

THE KEY FORMULAS6 TOOLS

\begin{gathered} \% \text{ change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100 \\ \text{Profit \%} = \frac{SP - CP}{CP} \times 100 \\ SP = MP \times \left(1 - \frac{d}{100}\right) \end{gathered}

1. Find the BasePercent of what? Change: the old value. Profit/loss: the cost price. Discount: the marked price.

2. Divide by the BaseDifference ÷ base, then × 100 to turn it into a percentage.

3. One Step at a TimeFor successive changes, apply each % to the new amount, never add the percentages.

Step-by-Step Worked Example

HAND-HOLDING TUTORIAL

OUR PROBLEM TO SOLVE

A shopkeeper buys a jacket for ₹800, marks it 25% above the cost price, and then gives a 10% discount. Find the selling price and the profit percentage.

STEP 01 • MARKED PRICE

MP = 800 + 25\% \text{ of } 800 = 800 \times 1.25 = 1000

STEP 02 • SELLING PRICE AFTER THE DISCOUNT

The discount is taken on the marked price, not the cost price:

SP = 1000 \times \left(1 - \frac{10}{100}\right) = 1000 \times 0.9 = 900

STEP 03 • PROFIT PERCENTAGE

\text{Profit} = SP - CP = 900 - 800 = 100

\text{Profit \%} = \frac{100}{800} \times 100 = 12.5\%

Notice it is not 25% − 10% = 15%: the two percentages have different bases.

FINAL CONCLUSION

SP = ₹900, profit = 12.5%

SP = 900, \qquad \text{Profit} = 12.5\%

The calculator below opens on this sale (CP 800, SP 900). Switch tool to try successive discounts.

LABORATORY

Interactive Percentage Calculator

LABORATORY

Percentage Engine

What do you want to work out?

Cost price (CP)Selling price (SP)Currency

Common Questions

How do you calculate percentage change?

Subtract the old value from the new one, divide by the old value, and multiply by 100:

\frac{\text{new} - \text{old}}{\text{old}} \times 100

. From 80 to 100 is a 25% increase; from 100 to 80 is a 20% decrease.

Is profit percentage calculated on cost price or selling price?

On the cost price:

\text{Profit \%} = \frac{SP - CP}{CP} \times 100

. Loss % is also on the cost price.

Are two discounts of 20% and 10% the same as 30%?

No. The second discount comes off the already reduced price: 1000 → 800 → 720, a total of 28%. The single equivalent discount is

a + b - \frac{ab}{100} = 20 + 10 - 2 = 28\%

What is the difference between markup and margin?

Both use the same gain (selling price − cost). Markup divides it by the cost; margin divides it by the selling price. Buying at 80 and selling at 100 is a 25% markup but a 20% margin.

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UNIT 10 • INTEREST & FINANCE

Percentage Calculator
Change, Profit & Loss, Discount

THE KEY FORMULAS6 TOOLS

\begin{gathered} \% \text{ change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100 \\ \text{Profit \%} = \frac{SP - CP}{CP} \times 100 \\ SP = MP \times \left(1 - \frac{d}{100}\right) \end{gathered}

1. Find the BasePercent of what? Change: the old value. Profit/loss: the cost price. Discount: the marked price.

2. Divide by the BaseDifference ÷ base, then × 100 to turn it into a percentage.

3. One Step at a TimeFor successive changes, apply each % to the new amount, never add the percentages.

Step-by-Step Worked Example

HAND-HOLDING TUTORIAL

OUR PROBLEM TO SOLVE

A shopkeeper buys a jacket for ₹800, marks it 25% above the cost price, and then gives a 10% discount. Find the selling price and the profit percentage.

STEP 01 • MARKED PRICE

MP = 800 + 25\% \text{ of } 800 = 800 \times 1.25 = 1000

STEP 02 • SELLING PRICE AFTER THE DISCOUNT

The discount is taken on the marked price, not the cost price:

SP = 1000 \times \left(1 - \frac{10}{100}\right) = 1000 \times 0.9 = 900

STEP 03 • PROFIT PERCENTAGE

\text{Profit} = SP - CP = 900 - 800 = 100

\text{Profit \%} = \frac{100}{800} \times 100 = 12.5\%

Notice it is not 25% − 10% = 15%: the two percentages have different bases.

FINAL CONCLUSION

SP = ₹900, profit = 12.5%

SP = 900, \qquad \text{Profit} = 12.5\%

The calculator below opens on this sale (CP 800, SP 900). Switch tool to try successive discounts.

LABORATORY

Interactive Percentage Calculator

LABORATORY

Percentage Engine

What do you want to work out?

Cost price (CP)Selling price (SP)Currency

Common Questions

How do you calculate percentage change?

Subtract the old value from the new one, divide by the old value, and multiply by 100:

\frac{\text{new} - \text{old}}{\text{old}} \times 100

. From 80 to 100 is a 25% increase; from 100 to 80 is a 20% decrease.

Is profit percentage calculated on cost price or selling price?

On the cost price:

\text{Profit \%} = \frac{SP - CP}{CP} \times 100

. Loss % is also on the cost price.

Are two discounts of 20% and 10% the same as 30%?

No. The second discount comes off the already reduced price: 1000 → 800 → 720, a total of 28%. The single equivalent discount is

a + b - \frac{ab}{100} = 20 + 10 - 2 = 28\%

What is the difference between markup and margin?

Both use the same gain (selling price − cost). Markup divides it by the cost; margin divides it by the selling price. Buying at 80 and selling at 100 is a 25% markup but a 20% margin.

PreviousCoordinate Geometry

Unit 10•45 of 47

NextSimple & Compound Interest

Percentage Calculator Change, Profit & Loss, Discount

Step-by-Step Worked Example

SP = ₹900, profit = 12.5%

Interactive Percentage Calculator

Percentage Engine

Common Questions

NETZ Engine

Percentage Calculator Change, Profit & Loss, Discount

Step-by-Step Worked Example

SP = ₹900, profit = 12.5%

Interactive Percentage Calculator

Percentage Engine

Common Questions

Percentage Calculator
Change, Profit & Loss, Discount

Percentage Calculator
Change, Profit & Loss, Discount