The price of petrol increases by 20%, by what percent a motor rider must decrease his consumption so that net expenditure can go up by 8% only

Question: The price of petrol increases by 20%, by what percent a motor rider must decrease his consumption so that net expenditure can go up by 8% only?

• 10 %
• 8 %
• 5 % 
• 4 % 

Answer: 

Solution: 

• $A =$ Percentage increase in price (+20%)
• $B =$ Required percentage decrease in consumption (?)
• Net expenditure increase = 8%

AB METHOD: -

$$8 = 20 + B + \frac{(20 \times B)}{100}$$

Multiply by 100 to clear the fraction:

$$8 \times 100 = 20 \times 100 + B \times 100 + 20B$$ $$800 = 2000 + 100B + 20B$$ $$800 - 2000 = 120B$$ $$-1200 = 120B$$ $$B=\frac{-1200}{120}=-10\mathrm{\%}$$

"_" The motor rider must decrease his consumption by 10% to ensure that his net expenditure increases by only 8%.

Detail Solution:

We are given that the price of petrol increases by 20%, and we need to find by what percentage the motor rider must decrease his consumption so that the net expenditure increases by only 8%.

Step 1: (Understand the Formula )(AB Method)

The formula for percentage change in expenditure is:

$$\text{Net Percentage Change} = A + B + \frac{A \times B}{100}$$

where:

• $A$ = Percentage increase in price (+20%)
• $B$ = Required percentage decrease in consumption (?)
• Net percentage change in expenditure = +8%

Step 2: (Set Up the Equation)

Using the formula:

$$8 = 20 + B + \frac{(20 \times B)}{100}$$

 Step 3: (Solve for $B)$

Multiply Everything by 100 to Eliminate the Fraction

$$8 \times 100 = (20 + B) \times 100 + (20 \times B)$$ $$800 = 2000 + 100B + 20B$$ $$800 = 2000 + 120B$$

Rearrange the Equation

$$800 - 2000 = 120B$$ $$-1200 = 120B$$

Divide by 120

$$B = \frac{-1200}{120}$$ $$B = -10\%$$

Step 4: (Interpret the Answer)

A negative percentage means a decrease in consumption.
So, the motor rider must decrease his consumption by 10% so that the net expenditure increases by only 8%.

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