Solved Exercises on Money Word Problems for Class 5

Master complex money word problems: addition, subtraction, multiplication, division, percentages, and mixed operations through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Percentage discount
Exercise 1
A store offers a 20% discount on a jacket that costs $80. How much does the jacket cost after the discount?
Definition:

Percentage discount: Reducing the original price by a certain percentage

Discount calculation method:
  1. Find the discount amount: Original Price × (Discount % ÷ 100)
  2. Subtract discount from original price
  3. Alternatively: Original Price × (1 - Discount % ÷ 100)
Original price
$80.00
Discount amount
$16.00
Final price
$64.00
Step 1: Calculate the discount amount

Discount = $80.00 × (20 ÷ 100)

Discount = $80.00 × 0.20

Discount = $16.00

Step 2: Subtract discount from original price

Final price = $80.00 - $16.00

Final price = $64.00

Step 3: Alternative method

Final price = $80.00 × (1 - 0.20)

Final price = $80.00 × 0.80

Final price = $64.00

Step 4: Verify the calculation

$64.00 + $16.00 = $80.00 ✓

$80.00 × (1 - 0.20) = $64.00
Final answer:

The jacket costs $64.00 after the discount.

Applied rules:

• Percentage conversion: 20% = 20 ÷ 100 = 0.20

• Discount formula: Discount = Original Price × Rate

• Final price: Original - Discount OR Original × (1 - Rate)

Tip: 10% of any amount is found by moving decimal point one place left.
Common mistake: Confusing discount amount with final price.
2 Tax calculation
Exercise 2
Lisa bought a book for $24.50. If the sales tax rate is 8%, how much tax does she pay? What is the total cost?
Definition:

Sales tax: Additional charge added to purchases based on a percentage of the purchase price

Purchase price
$24.50
Tax amount
$1.96
Total cost
$26.46
Step 1: Calculate the tax amount

Tax = $24.50 × (8 ÷ 100)

Tax = $24.50 × 0.08

Tax = $1.96

Step 2: Calculate the total cost

Total = Purchase price + Tax

Total = $24.50 + $1.96

Total = $26.46

Step 3: Alternative method for total

Total = $24.50 × (1 + 0.08)

Total = $24.50 × 1.08

Total = $26.46

Step 4: Verify the calculation

$24.50 + $1.96 = $26.46 ✓

Tax: $24.50 × 0.08 = $1.96, Total: $24.50 + $1.96 = $26.46
Final answer:

Lisa pays $1.96 in tax. The total cost is $26.46.

Applied rules:

• Tax calculation: Tax = Base Amount × Tax Rate

• Total with tax: Total = Base Amount + Tax

• Alternative total: Total = Base Amount × (1 + Tax Rate)

Tip: To find 1% of any amount, move decimal point two places left.
Common mistake: Adding tax rate as a whole number instead of decimal.
3 Exchange rate problem
Exercise 3
If 1 USD equals 0.85 EUR, how many euros can you get for $75? How many dollars do you need to get €51?
Definition:

Exchange rate: The value of one currency compared to another currency

USD to EUR
63.75 EUR
EUR to USD
60 USD
Step 1: Convert USD to EUR (Part A)

Given: 1 USD = 0.85 EUR

For $75: $75 × 0.85 EUR/USD = 63.75 EUR

Step 2: Convert EUR to USD (Part B)

To find how many USD for €51, we need the inverse rate

If 1 USD = 0.85 EUR, then 1 EUR = 1 ÷ 0.85 USD = 1.1765 USD

For €51: €51 × 1.1765 USD/EUR = 60 USD

Step 3: Verify the conversions

Check: 60 USD × 0.85 EUR/USD = 51 EUR ✓

Step 4: Alternative method for Part B

Using proportion: 1 USD / 0.85 EUR = x USD / 51 EUR

x = (1 × 51) ÷ 0.85 = 60 USD

$75 USD = 63.75 EUR, €51 = 60 USD
Final answer:

You can get 63.75 euros for $75. You need $60 to get €51.

Applied rules:

• Direct conversion: Multiply by exchange rate to convert to target currency

• Inverse conversion: Divide by exchange rate or multiply by reciprocal

• Proportion method: Set up ratios to solve currency conversion problems

Tip: When converting, multiply by the rate that cancels out the original currency.
Common mistake: Using the wrong direction for conversion (multiplying vs dividing).
Advanced Money Operations Guide
\text{Discount} = \text{Price} \times \frac{\text{Rate}}{100}
Discount Calculation
Discount
D = P × R%
Finding reduction amount
Tax
T = P × R%
Finding additional charge
Exchange
A_2 = A_1 × R
Converting currencies
Percentage
\frac{P}{100}
Converting to decimal
Key definitions:

Percentage: A fraction with denominator 100 (e.g., 25% = 25/100 = 0.25)

Discount: Reduction in price, usually expressed as a percentage

Tax: Additional charge added to purchases, usually expressed as a percentage

Exchange rate: Value of one currency in terms of another

Advanced Money Problem Solving Steps:
  1. Identify type: Determine if it's discount, tax, exchange, or mixed problem
  2. Extract data: List all given values and units
  3. Select formula: Choose appropriate calculation method
  4. Convert units: Ensure consistent units (percent to decimal)
  5. Calculate: Perform the mathematical operation
  6. Verify: Check if the answer makes sense in context
Tip 1: To find 10% of any amount, move decimal point one place left.
Tip 2: To find 1% of any amount, move decimal point two places left.
Tip 3: 50% means half, 25% means one-fourth, 75% means three-fourths.
Tip 4: For exchange rates, multiply to convert to stronger currency, divide for weaker.
Common errors: Forgetting to convert percentages to decimals, wrong operation direction in exchange rates.
Key formulas: Discount = Price × Rate, Total = Base × (1 + Tax Rate), Exchange = Amount × Rate.
Advanced Money Rules:

• Percentage conversion: X% = X ÷ 100 = decimal form

• Discount calculation: Final price = Original × (1 - Discount rate)

• Tax calculation: Total = Base × (1 + Tax rate)

• Exchange conversion: Multiply by rate to get target currency

• Verification: Always check if your answer makes sense in real-world context

Solution: Exercises 4 to 5
4 Interest calculation
Exercise 4
Sam deposits $500 in a savings account that earns 4% simple interest annually. How much interest does he earn in 3 years? What is the total amount in the account?
Definition:

Simple interest: Interest calculated only on the original principal amount

Principal
$500.00
Interest earned
$60.00
Total amount
$560.00
Step 1: Identify the variables

Principal (P) = $500.00

Rate (R) = 4% = 0.04

Time (T) = 3 years

Step 2: Apply the simple interest formula

Simple Interest = Principal × Rate × Time

Interest = $500.00 × 0.04 × 3

Interest = $20.00 × 3

Interest = $60.00

Step 3: Calculate the total amount

Total Amount = Principal + Interest

Total Amount = $500.00 + $60.00

Total Amount = $560.00

Step 4: Verify the calculation

Year 1: $500.00 × 0.04 = $20.00

Year 2: $500.00 × 0.04 = $20.00

Year 3: $500.00 × 0.04 = $20.00

Total: $20.00 × 3 = $60.00 ✓

Interest = $500.00 × 0.04 × 3 = $60.00, Total = $560.00
Final answer:

Sam earns $60.00 in interest. The total amount in the account is $560.00.

Applied rules:

• Simple interest formula: I = PRT

• Interest calculation: Interest = Principal × Rate × Time

• Total amount: A = P + I

Tip: Simple interest is always calculated on the original principal, not on accumulated interest.
Common mistake: Confusing simple interest with compound interest.
5 Profit and loss problem
Exercise 5
A shopkeeper bought a bicycle for $120 and sold it for $150. What is the profit? What is the profit percentage? Later, he bought another bicycle for $200 and sold it for $180. What is the loss and loss percentage?
Definition:

Profit: When selling price is greater than cost price

Loss: When selling price is less than cost price

First bicycle
Profit $30 (25%)
Second bicycle
Loss $20 (10%)
Step 1: Calculate profit for first bicycle

Cost Price = $120

Selling Price = $150

Profit = Selling Price - Cost Price = $150 - $120 = $30

Step 2: Calculate profit percentage for first bicycle

Profit % = (Profit ÷ Cost Price) × 100

Profit % = ($30 ÷ $120) × 100 = 0.25 × 100 = 25%

Step 3: Calculate loss for second bicycle

Cost Price = $200

Selling Price = $180

Loss = Cost Price - Selling Price = $200 - $180 = $20

Step 4: Calculate loss percentage for second bicycle

Loss % = (Loss ÷ Cost Price) × 100

Loss % = ($20 ÷ $200) × 100 = 0.10 × 100 = 10%

Step 5: Verify the calculations

Profit check: $120 + $30 = $150 ✓

Loss check: $200 - $20 = $180 ✓

Bicycle 1: $30 profit (25%), Bicycle 2: $20 loss (10%)
Final answer:

First bicycle: $30 profit (25% profit). Second bicycle: $20 loss (10% loss).

Applied rules:

• Profit formula: Profit = SP - CP (when SP > CP)

• Loss formula: Loss = CP - SP (when CP > SP)

• Percentage formulas: Profit/Loss % = (Profit/Loss ÷ CP) × 100

Tip: Always use Cost Price as the base for percentage calculations.
Common mistake: Using Selling Price instead of Cost Price for percentage calculations.
Advanced Money Concepts Summary
I = PRT
Simple Interest Formula
Key definitions:

Simple Interest: Interest calculated only on the principal amount

Compound Interest: Interest calculated on principal plus accumulated interest

Profit: Positive difference between selling price and cost price

Loss: Negative difference between selling price and cost price

Advanced methodology:
  1. Problem identification: Recognize whether it's discount, tax, interest, or profit/loss
  2. Data extraction: Identify all relevant values and units
  3. Formula selection: Choose appropriate formula based on problem type
  4. Unit conversion: Convert percentages to decimals, ensure consistent units
  5. Calculation: Apply the formula accurately
  6. Verification: Check if the answer makes logical sense
Tip 1: For quick percentage calculations, break down complex percentages (e.g., 15% = 10% + 5%).
Tip 2: Always verify that your answer is reasonable in the context of the problem.
Tip 3: In profit/loss problems, the base for percentage calculations is always the Cost Price.
Tip 4: When dealing with multiple currencies, keep track of which currency you're converting to.
Common errors: Incorrect percentage conversion, wrong base for percentage calculations, misreading exchange rates.
Real-world applications: Banking, shopping, investing, international trade, business calculations.
Advanced Money Rules:

• Interest calculation: I = PRT (Principal × Rate × Time)

• Discount rule: Final Price = Original × (1 - Discount Rate)

• Tax rule: Total = Base × (1 + Tax Rate)

• Profit/Loss: Always calculate percentage based on Cost Price

• Verification: Cross-check your answer with the original problem

Detailed Summary: Money Word Problems for Class 5

1. Core Concepts and Definitions
  • Percentage: A way to express a number as a fraction of 100. To convert percentage to decimal, divide by 100 (e.g., 25% = 0.25)
  • Discount: A reduction in the original price of an item, usually expressed as a percentage of the original price
  • Sales Tax: An additional charge added to purchases, calculated as a percentage of the purchase price
  • Exchange Rate: The value of one currency expressed in terms of another currency
  • Simple Interest: Interest calculated only on the original principal amount, not on previously earned interest
  • Profit: The amount gained when selling price is greater than cost price
  • Loss: The amount lost when selling price is less than cost price
2. Core Rules and Formulas
  • Percentage Conversion: X% = X ÷ 100 = Decimal Form
  • Discount Calculation: Discount Amount = Original Price × (Discount % ÷ 100)
  • Final Price After Discount: Final Price = Original Price × (1 - Discount Rate)
  • Tax Calculation: Tax Amount = Base Price × (Tax % ÷ 100)
  • Total with Tax: Total = Base Price × (1 + Tax Rate)
  • Simple Interest: I = PRT (where I = Interest, P = Principal, R = Rate, T = Time)
  • Profit: Profit = Selling Price - Cost Price (when SP > CP)
  • Loss: Loss = Cost Price - Selling Price (when CP > SP)
  • Profit/Loss Percentage: (Profit/Loss ÷ Cost Price) × 100
3. Step-by-Step Problem-Solving Methods
  • Step 1 - Identify the Problem Type: Determine if it's discount, tax, interest, exchange rate, profit/loss, or a combination
  • Step 2 - Extract Given Information: List all known values and identify what needs to be found
  • Step 3 - Select Appropriate Formula: Choose the correct formula based on the problem type
  • Step 4 - Convert Units: Ensure all percentages are converted to decimals and units are consistent
  • Step 5 - Perform Calculations: Apply the formula carefully, following order of operations
  • Step 6 - Verify Answer: Check if the answer makes sense in the context of the problem
4. Examples: Simple to Complex
  • Simple Example: Find 10% of $50 → $50 × 0.10 = $5.00
  • Intermediate Example: $100 with 15% tax → $100 × 1.15 = $115.00
  • Complex Example: $500 at 4% annual interest for 3 years → $500 × 0.04 × 3 = $60 interest
  • Advanced Example: Profit percentage when buying for $80 and selling for $100 → (($100-$80)÷$80)×100 = 25%
5. Tips, Tricks, and Common Pitfalls
  • Tips:
    • For quick 10% calculation, move decimal point one place left
    • For 1% calculation, move decimal point two places left
    • Break down complex percentages (e.g., 15% = 10% + 5%)
    • Always use Cost Price as the base for profit/loss percentage calculations
  • Common Mistakes:
    • Forgetting to convert percentages to decimals before calculation
    • Using Selling Price instead of Cost Price for profit/loss percentage
    • Misreading exchange rates (direction of conversion)
    • Mixing up discount amount with final price
6. Key Notes for Memorization
  • Memory Aid: "PRT" for Simple Interest formula (Principal × Rate × Time)
  • Memory Aid: "UP = Profit, DOWN = Loss" (compare Selling Price to Cost Price)
  • Memory Aid: "Base is always Cost Price" for percentage calculations
  • Memory Aid: "After Discount = Original × (1 - Rate)"
  • Memory Aid: "With Tax = Base × (1 + Rate)"
7. Real-World Applications
  • Shopping with discounts and sales tax
  • Banking and savings accounts with interest
  • International travel and currency exchange
  • Business transactions (buying/selling with profit/loss)
  • Investment decisions and financial planning

Questions & Answers

Question: I'm having trouble with percentage problems. How do I know when to multiply by the decimal and when to divide? It seems confusing.

Answer: Great question! Here's a clear system:

  • To find a percentage OF an amount: Multiply the amount by the decimal
  • Example: 20% of $50 → $50 × 0.20 = $10

When to divide: Usually when you know the percentage amount and need to find the original total

  • Example: If $15 is 25% of the original amount, find the original: $15 ÷ 0.25 = $60

Key phrase: "percent OF" → Multiply by decimal

Memory trick: "OF means MULTIPLE" (think "20% OF $50")

Always ask yourself: "Am I finding a part of the whole, or the whole itself?"

Question: When calculating profit or loss, why do we always use the Cost Price as the base for percentage calculations instead of Selling Price?

Answer: This is a fundamental principle in business and finance:

  • Cost Price is the reference point: It represents the investment or original value
  • Profit/Loss measures performance: It shows how well the investment performed
  • Consistency: Using Cost Price ensures standard comparison across different transactions

Think of it this way: "How much did I gain or lose relative to what I invested?"

Example: Bought for $100, sold for $120

  • Correct: ($120-$100)÷$100 × 100 = 20% profit
  • Incorrect: ($120-$100)÷$120 × 100 = 16.67% (wrong reference)

The industry standard is to measure returns against the initial investment!

Question: How can I quickly estimate percentages in my head without a calculator? Are there any shortcuts?

Answer: Yes! Here are some excellent mental math shortcuts:

  • 10%: Move decimal point one place left (e.g., $45.00 → $4.50)
  • 5%: Half of 10% (e.g., $4.50 ÷ 2 = $2.25)
  • 1%: Move decimal point two places left (e.g., $45.00 → $0.45)
  • 20%: Double 10% (e.g., $4.50 × 2 = $9.00)

For more complex percentages, break them down:

  • 15%: 10% + 5%
  • 25%: 20% + 5% OR half of 50%
  • 18%: 20% - 2% (which is 2 × 1%)

Example: 15% of $60

  • 10% of $60 = $6.00
  • 5% of $60 = $3.00
  • 15% = $6.00 + $3.00 = $9.00

These shortcuts will help you estimate quickly and check your work!

Question: What's the difference between simple interest and compound interest? We learned about simple interest, but I heard compound interest is more common.

Answer: Excellent question! Here's the key difference:

  • Simple Interest: Interest is calculated only on the original principal amount
  • Compound Interest: Interest is calculated on the principal plus previously earned interest

Example with $100 at 10% interest for 2 years:

  • Simple Interest: Year 1: $10, Year 2: $10, Total: $20
  • Compound Interest: Year 1: $10 (total $110), Year 2: $11 (10% of $110), Total: $21

For class 5, focus on simple interest (I = PRT), but compound interest is indeed more common in real banking because it grows faster. Simple interest is easier to calculate and understand, which is why it's taught first!

Question: When doing currency exchange, how do I know whether to multiply or divide by the exchange rate?

Answer: Think about the relationship and units:

  • From base currency to target currency: Multiply by the exchange rate
  • From target currency to base currency: Divide by the exchange rate

Example: If 1 USD = 0.85 EUR

  • USD to EUR: $100 × 0.85 = 85 EUR
  • EUR to USD: 85 EUR ÷ 0.85 = 100 USD

Alternative method: Set up a proportion:

  • 1 USD / 0.85 EUR = x USD / 85 EUR
  • x = (1 × 85) ÷ 0.85 = 100 USD

The key is to cancel out the currency you don't want and keep the one you need!