Question

One year, sales increased by 15%. The following year sales increased by 18%. Calculate the overall percentage increase in sales.

Answer 1

35.7%

Explanation:

Sales increase in Year 1

• Let the original sales be x
• Sales has increased by 15%
• Therefore, new sales will be :
• Original sales + Original sales x 15%
• ⇒ x (1 + 15%)
• ⇒ x (1 + 0.15)
• ⇒ x (1.15)
• ⇒ 1.15x

Sales increase in Year 2

• From Year 1, it has increased by 18%
• New sales will be :
• Year 1 sales + Year 1 sales x 18%
• ⇒ 1.15x (1 + 18%)
• ⇒ 1.15x (1 + 0.18)
• ⇒ 1.15x (1.18)
• ⇒ 1.357x

Overall Increase

• Year 2 sales - Original sales / Original sales
• 1.357x - x / x
• 0.357x / x
• 0.357
• Decimal to % ⇒ x 100%
• 0.357 x 100%
• 35.7%

Answer 2

First year (Year 1):

Let the sales be known as "a".

Given statement:

One year, sales increased by 15%.

This can be written as:

• Year 1 = a + (a × 15%)

Step-1: Evaluate the percentage

• ⇒ Year 1 = a + (a × 15%)
• ⇒ Year 1 = a + (a × 15/100)

Step-2: Multiply the terms inside the parentheses

• ⇒ Year 1 = a + (a × 15/100)
• ⇒ Year 1 = a + (15a/100)

Step-3: Open the parentheses

• ⇒ Year 1 = a + (15a/100)
• ⇒ Year 1 = 100a/100 + 15a/100

Step-4: Add the like terms;

• ⇒ Year 1 = 100a/100 + 15a/100
• ⇒ Year 1 = 115a/100

Next year (Year 2):

Given statement:

The following year sales increased by 18%.

This can be written as:

• Year 2 = Year 1 + (Year 1 × 18%)

Step-1: Substitute the amount of sales in year 1:

• ⇒ Year 2 = Year 1 + (Year 1 × 18%)
• ⇒ Year 2 = 115a/100 + (115a/100 × 18/100)

Step-2: Simplify the fractions in the parentheses:

• ⇒ Year 2 = 115a/100 + (115a/100 × 18/100)
• ⇒ Year 2 = 115a/100 + (23a/20 × 9/50)

Step-3: Multiply the fractions in the parentheses:

• ⇒ Year 2 = 115a/100 + (23a/20 × 9/50)
• ⇒ Year 2 = 1150a/1000 + (207a/1000)

Step-4: Open the parenthesis:

• ⇒ Year 2 = 1150a/1000 + (207a/1000)
• ⇒ Year 2 = 1150a/1000 + 207a/1000

Step-5: Add the fractions:

• ⇒ Year 2 = 1150a/1000 + 207a/1000
• ⇒ Year 2 = 1357a/1000

Overall percentage increase:

Formula:

Overal percentage increase = (Sales in year 2 - Original sales) × 100

Step-1: Substitute the values in the equation:

• ⇒ Overal percentage increase = (Sales in year 2 - Original sales) × 100
• ⇒ Overal percentage increase = (1357a/1000 - a) × 100

Step-2: Simplify the expression in the parentheses:

• ⇒ Overal increase = (1357a/1000 - a) × 100
• ⇒ Overal increase = (1357a/1000 - 1000a/1000) × 100
• ⇒ Overal increase = (357a/1000) × 100

Step-3: Open the parentheses and simplify:

• ⇒ Overal increase = (357a/1000) × 100
• ⇒ Overal increase = 357a/10
• ⇒ Overal increase = 35.7a

Step-4: Determine the overal increase in percentage:

• ⇒ Overal increase = 35.7a
• ⇒ Overal percentage increase = 35.7%

Therefore, the overal increase in percent is 35.7%.