Percentages in Shopping Discounts
Irresistible offers? Thanks to the percentage! Easily calculate how much you'll save.
- 🛍️ S/200 with 25% discount → you pay S/150.
- 💥 “70% OFF” means a big discount off the original price.
Free Online Percentage Calculators
Calculate percentages, discounts, increases, fees, and more — all in one place.
Simple tools to help you make fast and accurate percentage calculations online.
Discount Calculator
Simple
Example: Simple
a store discount
If a product costs
and has
%
discount,
The final price is
$
Double Discount Calculator
Example: a store discount + an extra coupon discount
If a product costs
and has a store discount of
%
and you also have a coupon of
%
off,
Calculadora de Cuota Inicial
Ejemplo: si un departamento cuesta S/ 350,000 y debes pagar 10% de inicial
Si el departamento cuesta
y debo pagar una inicial del
%
What Are Percentage Calculators?
Percentage calculators are tools that help you find increases, decreases, and proportions without doing manual math. They’re perfect for everyday use — from calculating discounts when shopping to figuring out business growth, taxes, or investment returns.
Quick Percentage Calculator
Try a quick example below 👇
Uses of Percentages
Percentages in Finance and Economics
Percentages drive the world of money: interest, inflation, taxes... everything!
- 💰 8% interest on S/1000 → you earn S/80 per year.
- 📉 6% inflation reduces your purchasing power.
Percentages in Statistics
Surveys? Data? Percentages tell stories without a thousand numbers.
- 📊 72% say “Yes” → 3 out of 4 agree.
- 🚬 18% smoke → social analysis in action.
Percentages in Education
Pass or fail? Percentages tell you if you made it.
- 📘 45 out of 50 points → 90% grade!
- 🎯 At least 70% required to pass a subject.
Percentages in Health
From body fat to medical effectiveness, percentages help take care of your health too!
- 💪 22% body fat: within the healthy range.
- 💊 Treatment effective in 85% of cases.
Percentages in Everyday Life
Percentages save you at the restaurant or in the kitchen—literally!
- 🍽️ 10% tip on S/150 → you leave S/15.
- 👨🍳 Cooking for 2 → cut the recipe by 50%.
Percentage Calculators
Simple Percentage
What is
of
?
%
| 500 | 100 |
Total: 500
25%
75%
125
375
Percentage of a Total
If
is
, then the total is:
%
| 100 |
Total: 200
25%
75%
50
150
Percentage of an Amount
If the total is
then
, represents:
%
Total: 200
25%
75%
40
160
Percentage Change
If
%
is
, then:
%
Total: 16.67
20%
80%
40
160
Tips for Solving Percentage Problems
Learn to handle percentages with these practical tips that will help you solve any exercise quickly and confidently.
Use the Base Formula
Remember that the percentage of a quantity is calculated
as:
(percentage × quantity) / 100.
This is the foundation for all problems of this type.
Identify if it's an Increase or a Decrease (Discount)
If the value grows (interest, bonus, taxes), the percentage is added. If it decreases (sales, losses, discounts), the percentage is subtracted.
Convert Percentages to Decimals
It is sometimes easier to work with decimals: 25% = 0.25, 10% = 0.10, 8% = 0.08. Multiply the number by the decimal to get the result.
Check Your Calculations
Always verify your steps: First, calculate the percentage, then add or subtract depending on the type of problem. A small error can change the entire result.
Practice with Real-Life Situations
Apply percentages in your daily life: store discounts, taxes, tips, yields, etc. This will reinforce your understanding practically.
Use a Calculator if Needed
Don't hesitate to use a calculator to confirm your math. Accuracy is important, especially in financial or scientific contexts.
Easy Level Percentage Exercises
Learn to calculate percentages step by step with basic examples and real-world cases.
Exercise 1 — What is 25% of S/200?
We want to calculate how much 25% of a total value of S/200 represents.
| Total Value | S/200 |
|---|---|
| Percentage | 25% |
Step 1: Set up
the
proportion: 100% → S/200; 25% → x
Step 2: Apply the
rule
of three:
x = (25 × 200) / 100Step 3: Result:
x = S/50
✅ 25% of S/200 is S/50.
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Exercise 2 — 30% Discount on S/150
We want to calculate the final price after applying a 30% discount.
| Original Price | S/150 |
|---|---|
| Discount | 30% |
Step 1: Discount:
x = (30 × 150) / 100 = S/45
Step 2: Final
Price:
150 − 45 = S/105
💰 Final price with discount: S/105.
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this
calculator
Exercise 3 — What percentage is 18 of 20?
Calculate the percentage that 18 represents out of a total of 20.
| Part | 18 |
|---|---|
| Total | 20 |
Step 1: Formula:
x = (18 × 100) / 20
Step 2: Result:
x = 90%
📊 18 out of 20 is equivalent to 90%.
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this
calculator
Exercise 4 — 10% Salary Increase
A worker earns S/2,500 and receives a 10% increase. What will be their new salary?
| Current Salary | S/2,500 |
|---|---|
| Increase | 10% |
Step 1: Increase:
(10 × 2500) / 100 = S/250
Step 2: New
Salary:
2500 + 250 = S/2750
💼 New salary: S/2,750.
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this
calculator
Exercise 5 — Body Fat Percentage
An athlete has 18 kg of body fat and weighs 80 kg. What percentage of their weight is fat?
| Total Weight | 80 kg |
|---|---|
| Body Fat | 18 kg |
Step 1: Formula:
(18 × 100) / 80 = 22.5%
🏋️♂️ Body fat represents 22.5%.
See
this
calculator
Exercise 6 — 18% Tax on a Purchase (IGV)
A laptop costs S/3,000 and an 18% sales tax (IGV) is applied. What will be the final price?
| Base Price | S/3,000 |
|---|---|
| IGV (Sales Tax) | 18% |
Step 1: Calculate
IGV:
(18 × 3000) / 100 = S/540
Step 2: Final
Price:
3000 + 540 = S/3,540
💻 Final price including IGV: S/3,540.
See
this
calculator
Exercise 7 — 12% Gas Price Increase
The price of gasoline was S/6.50 per liter. If it increases by 12%, what will be the new price?
| Initial Price | S/6.50 |
|---|---|
| Increase | 12% |
Step 1: Calculate
the
increase:
(12 × 6.50) / 100 = 0.78
Step 2: New
Price:
6.50 + 0.78 = S/7.28
⛽ The new price per liter of gasoline will be
S/7.28.
See
this
calculator
Exercise 8 — 15% Discount on Rent
An apartment costs S/1,800 per month, but a 15% promotional discount is applied. How much will be paid monthly?
| Original Price | S/1,800 |
|---|---|
| Discount | 15% |
Step 1:
Calculate the discount:
(15 × 1800) / 100 = 270
Step 2: Discounted
Price:
1800 - 270 = S/1,530
🏠 The monthly price with discount is S/1,530.
See
this
calculator
Exercise 9 — 25% Monthly Salary Savings
If a person earns S/2,800 per month and decides to save 25% of their salary, how much money do they save and how much is left to spend?
| Monthly Salary | S/2,800 |
|---|---|
| Savings Percentage | 25% |
Step 1: Calculate
savings:
(25 × 2800) / 100 = 700
Step 2: Remaining
Money:
2800 - 700 = S/2,100
🐷 Monthly Savings: S/700 | Available for
expenses:
S/2,100.
See
this
calculator
Exercise 10 — 30% Discount at a Clothing Store
A jacket costs S/250 and has a 30% discount. What is the final price?
| Original Price | S/250 |
|---|---|
| Discount | 30% |
Step 1: Discount:
(30 × 250) / 100 = 75
Step 2: Final
Price:
250 - 75 = S/175
👕 The final price of the jacket is S/175.
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this
calculator
Exercise 11 — 10% Interest on an Investment
You invest S/5,000 in a fund that generates a 10% annual interest. How much will you earn at the end of the year?
| Initial Capital | S/5,000 |
|---|---|
| Annual Interest | 10% |
Step 1: Interest
earned:
(10 × 5000) / 100 = 500
Step 2: Final total:
5000 + 500 = S/5,500
💰 Annual Gain: S/500 | Total:
S/5,500.
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calculator
Exercise 12 — 40% Discount on a Television
A television costs S/2,000 and is on sale with a 40% discount. How much do you pay?
| Original Price | S/2,000 |
|---|---|
| Discount | 40% |
Step 1: Discount amount:
(40 × 2000) / 100 = 800
Step 2: Final Price:
2000 - 800 = S/1,200
📺 Final Price of the TV: S/1,200.
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calculator
Exercise 13 — 10% Tip at a Restaurant
The total restaurant bill is S/180. If you leave a 10% tip, how much do you leave and what is the total amount you pay?
| Consumption Total | S/180 |
|---|---|
| Tip | 10% |
Step 1: Calculate
tip:
(10 × 180) / 100 = 18
Step 2: Total
to
pay:
180 + 18 = S/198
🍽️ Tip: S/18 | Total to Pay:
S/198.
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calculator
Exercise 14 — Final Grade with Weighting
A student gets 80% on exams (60% of the total) and 90% on assignments (40% of the total). What is their final grade?
| Exams | 80% (60% weight) |
|---|---|
| Assignments | 90% (40% weight) |
Step 1: Exams:
(80 × 60) / 100 = 48
Step 2: Assignments:
(90 × 40) / 100 = 36
Step 3:
Final
Grade:
48 + 36 = 84%
🎓 Final Grade: 84%.
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calculator
Exercise 15 — 25% Increase in Monthly Sales
A store sold S/40,000 in January. In February, its sales increased by 25%. How much did it sell in February?
| January Sales | S/40,000 |
|---|---|
| Increase | 25% |
Step 1:
Increase
amount:
(25 × 40000) / 100 = 10,000
Step 2:
February
Total:
40000 + 10000 = S/50,000
🛒 February Sales: S/50,000.
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calculator
Exercise 16 — 20% Reduction in Electricity Consumption
A household used to pay S/180 monthly for electricity and reduces its consumption by 20%. How much will they pay now?
| Previous Consumption | S/180 |
|---|---|
| Reduction | 20% |
Step 1:
Reduction:
(20 × 180) / 100 = 36
Step 2: New Payment:
180 - 36 = S/144
💡 New Monthly Payment: S/144.
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calculator
Exercise 17 — 20% Discount on Airplane Tickets
An airplane ticket costs S/1,200, but the airline offers a 20% discount for early purchase. How much will the passenger pay?
| Original Price | S/1,200 |
|---|---|
| Discount | 20% |
Step 1: Calculate
discount:
(20 × 1200) / 100 = 240
Step 2: Final Price:
1200 - 240 = S/960
✈️ The passenger will pay S/960 for their
ticket.
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calculator
Exercise 18 — 15% Reduction in Body Weight
A person weighed 80 kg and managed to reduce their weight by 15% with diet and exercise. What is their new weight?
| Initial Weight | 80 kg |
|---|---|
| Reduction | 15% |
Step 1: Weight
Loss:
(15 × 80) / 100 = 12
Step 2: New Weight:
80 - 12 = 68 kg
🏋️♀️ Current Weight: 68 kg.
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calculator
Exercise 19 — 10% Annual Depreciation on a Car
A new car costs S/60,000 and depreciates by 10% each year. What will its value be at the end of the first year?
| Initial Value | S/60,000 |
|---|---|
| Depreciation | 10% |
Step 1:
Loss
in
Value:
(10 × 60000) / 100 = 6,000Step 2: Final
Value:
60000 - 6000 = S/54,000
🚗 Car Value after 1 year: S/54,000.
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calculator
Exercise 20 — 12% Bonus on Salary
An employee earns S/3,500 monthly and receives a 12% bonus. How much will they collect in total that month?
| Base Salary | S/3,500 |
|---|---|
| Bonus | 12% |
Step 1: Calculate
bonus:
(12 × 3500) / 100 = 420
Step 2: Total to
collect:
3500 + 420 = S/3,920
💼 Monthly Total with Bonus: S/3,920.
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calculator
Key Tips for Medium Level Percentage Problems
Advance to the next level. Master successive operations, weighted calculation, and discount reversal, essential for more complex problems.
Multiply Variation Factors
When you have successive discounts or increases (e.g., -10% and then +5%), DO
NOT add or subtract them directly. Convert each one to its decimal factor and
then multiply them all.
Example: -10% is $0.90$. +5% is $1.05$. The total factor is $0.90$ times $1.05$.
Use the Weighted Percentage
If you have groups of different sizes (e.g., two batches of products with
different percentages of defects), don't average the percentages. You must
calculate the total part in each group and divide by the total overall.
The size of the group affects the final result.
Divide to Reverse Operations
To find the original price before a discount or increase (e.g., a tax) was
applied, you must divide the final value by the decimal factor. This is key in
problems where the initial amount is missing.
Example: If a price already includes a 10% VAT, divide the final price by
$1.10$.
The Percentage of a Percentage
To calculate the X% of Y% of a quantity, simply multiply the two percentages
converted to decimals. There's no need to calculate the first percentage on the
total and then calculate the second.
Example: 20% of 50% is equivalent to 10% of the total.
Beware of the Comparison Base
A common mistake is confusing the base. If a value A is 20% greater than B, this
does not mean that B is 20% less than A.
The variation formula always divides the difference by the initial value (the
comparison base). Always identify what the base is!
Markup to Nullify a Discount
If you applied a discount (e.g., 20%), the markup you need to apply to the
discounted price to return to the original is always greater than the discount.
This is because the markup is calculated on a smaller base (the discounted
price). To nullify a 20% discount, you need a 25% markup.
Intermediate Level Percentage Exercises
Learn to calculate percentages step by step with intermediate level examples and real-world cases.
Exercise 1 — Successive Discounts on Price
A television has a list price of S/1,500. The store applies two successive discounts: first a 20% for a promotion, and then an 10% additional discount on the already reduced price. What is the final price of the television?
| Initial Price | S/1,500 |
|---|---|
| 1st Discount | 20% |
| 2nd Discount | 10% |
Step 1: Calculate the
price
after the first discount (20%).
1500 × (1 - 0.20) = 1500 × 0.80 = 1,200
Step 2: Apply the
second
discount (10%) on the new price.
1200 × (1 - 0.10) = 1200 × 0.90 = 1,080
📺 Final Price of the TV: S/1,080.
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Exercise 2 — Find the Base Price before VAT
An invoice indicates that the final cost of a software, including the Value Added Tax (VAT) of 18%, is S/295. What was the original price of the software before applying the tax?
| Price with VAT | S/295 |
|---|---|
| VAT Rate | 18% |
Step 1: Determine the
price multiplication factor.
100% + 18% = 118% (or 1.18)
Step 2: Divide the final
price
by the factor to find the base price (Total).
295 / 1.18 = 250
🧾 Original Price (without VAT): S/250.
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calculator
Exercise 3 — Percentage Variation in Area
A rectangular plot measures 10 m wide and 20 m long. If the width is increased by 10% and the length is reduced by 10%. What is the percentage of area variation of the plot?
| Initial Area | $10 \times 20 = 200 m^2$ |
|---|---|
| Width Change | +10% |
| Length Change | -10% |
Step 1: Calculate
the
new dimensions.
Width: 10 × 1.10 = 11 m
Length: 20 × 0.90 = 18 m
Step 2: Calculate the
new
area.
Final Area: 11 m × 18 m = 198 m^2
Step 3: Calculate
the
Percentage Variation.
Variation = ((198 - 200) / 200) × 100 = -1%
📐 The area variation is a reduction of 1%.
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calculator
Exercise 4 — Solution Concentration
There are 20 liters of a solution containing 30% alcohol. If 5 liters of pure alcohol are added to the solution, what will be the new percentage concentration of alcohol in the final solution?
| Initial Volume | 20 liters |
|---|---|
| Initial Concentration | 30% alcohol |
| Alcohol Added | 5 liters |
Step 1: Calculate the
initial
alcohol amount.
Initial Alcohol: 20 liters × 0.30 = 6 liters
Step 2: Calculate
the
new total alcohol and the new total volume.
Final Alcohol: 6 liters + 5 liters = 11 liters
Final Volume: 20 liters + 5 liters = 25 liters
Step 3: Calculate the
new
concentration (Percentage).
Concentration: (11 liters / 25 liters) × 100 = 44%
🧪 The new alcohol concentration is 44%.
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calculator
Exercise 5 — Best Discount Option
A bicycle costs S/800. Store A offers a single discount of 30%. Store B offers two successive discounts of 20% and then 10%. Which store offers the bicycle at the lowest final price?
| Initial Price | S/800 |
|---|---|
| Option A | 30% (single) |
| Option B | 20% and then 10% |
Step 1: Calculate the price
at Store A.
Price A = 800 × (1 - 0.30) = 800 × 0.70 = 560
Step 2: Calculate the
price at Store B (successive discounts).
Price B = 800 × 0.80 × 0.90 = 800 × 0.72 = 576
Step 3:
Compare results.
S/560 (Store A) vs S/576 (Store B)
🛍️ The best option is Store A with a price of
S/560.
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calculator
Exercise 6 — Simple Annual Compound Interest
A person invests S/5,000 in an account that offers a fixed annual interest of 6%. If the money is not withdrawn, how much money will the investor have after two years? (Assume annual compounding).
| Initial Capital | S/5,000 |
|---|---|
| Annual Rate | 6% |
| Period | 2 years |
Step 1: Determine the
growth factor:
1 + 0.06 = 1.06
Step 2: Apply
the factor for two years (power).
Final Capital = 5000 × (1.06)²
Step 3: Calculate the
final result:
5000 × 1.1236 = 5,618
💰 Final Capital after 2 years: S/5,618.
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calculator
Exercise 7 — Population Projection (Total)
In an electoral survey of a city, it was determined that 22,500 people are under 30 years old. If it is known that this group represents exactly 45% of the city's total population, how many inhabitants does the city have in total?
| Part (Under 30) | 22,500 people |
|---|---|
| Percentage Represented | 45% |
Step 1: Apply the
formula to calculate the Total.
Total = (Part / Percentage) × 100
Step 2: Substitute the
values and calculate:
Total = (22500 / 45) × 100
Total = 500 × 100 = 50,000
🏘️ The total population of the city is 50,000
inhabitants.
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calculator
Exercise 8 — Percentage Profit on Cost
A merchant buys a batch of merchandise for S/4,000 (Cost). If they manage to sell all the merchandise for S/5,800 (Sale), what is the percentage profit they obtained with respect to the cost of the merchandise?
| Initial Cost | S/4,000 |
|---|---|
| Selling Price | S/5,800 |
Step 1: Calculate the
net Profit (Gain).
Profit = Sale - Cost = 5800 - 4000 = 1,800
Step 2: Calculate the
Profit as a percentage of the Cost (Total).
Percentage = (Profit / Cost) × 100
= (1800 / 4000) × 100 = 45%
💵 The profit is 45% over the initial cost.
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calculator
Exercise 9 — Percentage Reduction to Reach a Goal
A product is currently sold at S/160 . Management has set a goal to reduce the price to S/148 to be more competitive. What percentage must the discount be to reach this target price?
| Initial Price ($V_i$) | S/160 |
|---|---|
| Target Price ($V_f$) | S/148 |
Step 1: Calculate the
difference (discount amount).
Discount = Initial - Target = 160 - 148 = 12
Step 2: Calculate the
discount as a percentage of the initial price (Total).
Percentage = (Discount / Initial) × 100
= (12 / 160) × 100 = 7.5%
📉 The necessary discount must be 7.5% .
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calculator
Exercise 10 — Percentage of a Subgroup
In a factory of 800 employees, 60% work in production. Of the production employees, 25% are supervisors. How many employees in the factory are production supervisors ?
| Total Employees | 800 |
|---|---|
| % Production | 60% |
| % Supervisors (of Production) | 25% |
Step 1: Calculate the
number of employees in Production.
Production = 800 × 0.60 = 480
Step 2: Calculate the
supervisors (25% of Production employees).
Supervisors = 480 × 0.25 = 120
👨💼 The number of production supervisors is 120
people .
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calculator
Exercise 11 — Find the Base Price with Two Increases
The price of a stock is currently S/330 . This price is the result of the stock rising 10% last month and another 10% this month over last month's value. What was the price of the stock two months ago?
| Final Price | S/330 |
|---|---|
| 1st Increase | +10% (Factor 1.10) |
| 2nd Increase | +10% (Factor 1.10) |
Step 1: Determine the
cumulative growth factor.
Cumulative Factor = 1.10 × 1.10 = 1.21
Step 2: Divide
the final price by the cumulative factor to find the original (Inverse).
Original Price = 330 / 1.21 ≈ 272.73
📈 The original price of the stock was approximately
S/272.73 .
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calculator
Exercise 12 — Net Profit Calculation with Taxes
A service was sold for S/4,000 . The total cost to provide the service was S/2,800 . On the profit, the company must pay a tax of 15% . What was the net profit (after taxes)?
| Total Revenue | S/4,000 |
|---|---|
| Total Cost | S/2,800 |
| Tax on Profit | 15% |
Step 1: Calculate the
Gross Profit (before taxes).
Gross Profit = Revenue - Cost = 4000 - 2800 = 1,200
Step 2: Calculate the
retention factor (what remains after tax).
100% - 15% = 85% (or 0.85)
Step 3: Calculate the
Net Profit.
Net Profit = 1200 × 0.85 = 1,020
📊 The net (final) profit is S/1,020 .
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Exercise 13 — Final Price after Discount and Surcharge
A computer monitor costs S/1,200 . First, a 20% discount is applied for an event, and then the discounted price receives a 10% surcharge for shipping cost. What is the final price of the monitor?
| Initial Price | S/1,200 |
|---|---|
| 1st Operation | -20% (Discount) |
| 2nd Operation | +10% (Surcharge) |
Step 1: Apply the
20% discount.
Price with Discount = 1200 × (1 - 0.20) = 1200 × 0.80 = 960
Step 2: Apply the 10%
surcharge on the discounted price.
Final Price = 960 × (1 + 0.10) = 960 × 1.10 = 1,056
📦 The final price with discount and surcharge is S/1,056 .
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Exercise 14 — Quantity Needed for a Concentration
A chemist has 15 liters of a solution containing 20% acid. He wants to add pure water (0% acid) so that the new acid concentration is 15% . How many liters of water must he add?
| Initial Volume | 15 liters |
|---|---|
| Initial Concentration | 20% acid |
| Desired Final Concentration | 15% acid |
Step 1: Calculate
the
amount of acid (Part) that does NOT change.
Acid = 15 liters × 0.20 = 3 liters
Step 2: Use the inverse
percentage
formula to find the Final Total Volume.
Final Total Volume = Acid / Final Concentration = 3 / 0.15 = 20 liters
Step 3: Subtract the
initial volume to find the water added.
Water Added = 20 liters - 15 liters = 5 liters
💧 He must add 5 liters of pure water.
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Exercise 15 — Total Population by Subgroup Inference
In an assembly, 35% of attendees voted Yes and 40% voted No. If the remaining 50 people abstained (did not vote), how many attendees were there in total at the assembly?
| % Voted Yes | 35% |
|---|---|
| % Voted No | 40% |
| Abstentions (Part) | 50 people |
Step 1: Calculate the
percentage of Abstentions.
% Abstention = 100% - (35% + 40%) = 100% - 75% = 25%
Step 2: Use the inverse
percentage
formula to find the Total.
Total = (Part / Percentage) × 100
Total = (50 / 25) × 100 = 2 × 100 = 200
👥 The total number of attendees was 200 people .
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calculator
Exercise 16 — Sustained Population Growth
A city has a current population of 120,000 inhabitants . If the annual growth rate remains constant at 3% , what will the city's population be in two years ? (Assume compounded growth).
| Initial Population | 120,000 inhab. |
|---|---|
| Growth Rate | 3% annually |
| Period | 2 years |
Step 1: Determine the
growth factor:
1 + 0.03 = 1.03
Step 2: Apply
compounded growth for 2 years.
Final Population = 120000 × (1.03)²
Step 3: Calculate the
final result:
120000 × 1.0609 = 127,308
📈 Estimated population after 2 years: 127,308 inhabitants .
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calculator
Exercise 17 — Weighted Percentage in Groups
At a university, the main campus has 2,000 students, of which 40% are foreign. The satellite campus has 500 students, of which 60% are foreign. What is the total percentage of foreign students across both campuses?
| Total Students | 2500 |
|---|---|
| Main Campus (Foreign) | 40% of 2000 |
| Satellite Campus (Foreign) | 60% of 500 |
Step 1: Calculate the
number
of foreign students on each campus.
Main Campus: 2000 × 0.40 = 800
Satellite Campus: 500 × 0.60 = 300
Step 2: Calculate
the Total Foreign Students and the Grand Total.
Total Foreign = 800 + 300 = 1,100
Grand Total = 2000 + 500 = 2,500
Step 3: Calculate the
Total Percentage.
Percentage = (1100 / 2500) × 100 = 44%
🌎 The total percentage of foreign students is 44% .
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Exercise 18 — Find Price Before Discount and Surcharge
A pair of shoes has a final price of S/144 . It is known that this price resulted from applying a 20% discount to the original price, and then an 8% VAT (tax) on the already discounted price. What was the original price before any discount?
| Final Price | S/144 |
|---|---|
| 1st Operation (Discount) | -20% (Factor 0.80) |
| 2nd Operation (VAT/Surcharge) | +8% (Factor 1.08) |
Step 1: Reverse
the VAT (Divide by factor 1.08).
Discounted Price = 144 / 1.08 = 133.33
Step 2:
Reverse the discount (Divide by factor 0.80).
Original Price = 133.33 / 0.80 ≈ 166.67
💸 The original price before any operation was S/166.67 .
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Exercise 19 — Find the Total from the Variation Amount
A company's monthly revenue increased by S/1,200 this month compared to the previous month. If it is known that this increase represents exactly 6% of the previous month's revenue ($V_i$), what was the previous month's revenue?
| Amount of Increase (Part) | S/1,200 |
|---|---|
| % Increase | 6% |
| Total to Find ($V_i$) | Previous revenue |
Step 1: Apply the Inverse
Percentage formula where the Part is the Increase.
Total = (Part / Percentage) × 100
Step 2: Substitute
the
values.
Previous Revenue = (1200 / 6) × 100
= 200 × 100 = 20,000
🧾 The previous month's revenue was S/20,000 .
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Exercise 20 — Surcharge to Reverse Discount
The original price of a product was discounted by 20% . What surcharge percentage must be applied to the discounted price so that the final price is exactly equal to the original price?
| Initial Discount | 20% (Factor 0.80) |
|---|---|
| Initial Price (Total) | Assume 100 (or 1) |
| Discounted Price | 80 (or 0.8) |
Step 1:
Determine the difference (surcharge amount).
Original Price - Discounted Price = 100 - 80 = 20 (or $1 - 0.8 = 0.2$)
Step 2: Calculate the
Percentage Variation with respect to the Discounted Price (the new base).
Surcharge % = (Difference / Discounted Price) × 100
= (20 / 80) × 100 = 0.25 × 100 = 25%
🔄 The surcharge that must be applied is 25% on the discounted
price.
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