Increase or Decrease in Percent

Imagine your favourite chocolate bar costs ₹20 today, but next month it costs ₹25. How much has the price changed?

We use percentage change to express this change in a way that's easy to understand and compare.

Percentage change tells us how much a quantity has increased or decreased compared to its original value, expressed as a part of 100.

\[\text{Percentage Increase} = \frac{\text{Increase in Value}}{\text{Original Value}} \times 100\%\]

\[\text{Percentage Decrease}=\frac{\text{Decrease in Value}}{\text{Original Value}}\times100\%\]

• Step 1: Identify the original value and the new value
• Step 2: Calculate the change (increase or decrease)
• Step 3: Determine if it's an increase or decrease
• Step 4: Apply the appropriate formula
• Step 5: Calculate and express as a percentage

Problem: If the price of milk increases from ₹24 per litre to ₹32.40 per litre, find the percentage increase.

Solution:

• Step 1: Original price = ₹24, New price = ₹32.40

• Step 2: Increase in price = ₹32.40 - ₹24 = ₹8.40

• Step 3: This is an increase (new > original)

• Step 4: \[\text{Percentage Increase} = \frac{\text{Increase in Value}}{\text{Original Value}} \times 100\%\]

• Step 5: \[\frac{\text{8.40}}{\text{24}} \times 100\%\]

Answer: The price of milk increased by 35%.

Problem: Out of ₹36,000, two-fifths was kept in a bank. Of the remaining money, 40% is spent on food and 15% on rent. Find how much money is spent on food and rent.
Solution:

• Step 1: Money kept in bank =\[\frac{\text{2}}{\text{5}}\] × ₹36,000 = ₹14,400
  
  
• Step 2: Remaining money = ₹36,000 - ₹14,400 = ₹21,600
  
  
• Step 3: Money spent on food = 40% of ₹21,600 

                                                          = \[\frac{\text{40}}{\text{100}}\] × ₹21,600
                                                           =  ₹ 8,640

• Step 4: money spent on rent = 15% of ₹ 21,600
                                                 = \[\frac{\text{15}}{\text{100}}\] × ₹21,600
                                                 = ₹ 3,240

Answer: Food: ₹8,640, Rent: ₹3,240

• Always divide by the original value.

• For a 50% increase, multiply by 1.5; for a 25% decrease, multiply by 0.75.

• Label each step clearly using numbers.

• \[\text{Percentage Increase} = \frac{\text{New − Original}}{\text{Original}} \times 100\%\]
  
  
• \[\text{Percentage Decrease} = \frac{\text{ Original − New }}{\text{Original}} \times 100\%\]