Question

The number 4 is increased by a% to 5. Then the obtained number 5 is decreased by b% to 4 . Which of the following is true for the relationship between a and b?

• A. a > b
  
• B. a < b
  
• C. a = b
  

Answer 1

The correct option is A a > b


Step 1: Solving for a
Given, the number 4 is increased by a% to reach 5.

$\text{4 is increaded by a\% = 4 + 4}\text{a}\therefore 4+4\text{a}=54\text{a}=5-44\text{a}=1\text{a}=\frac{1}{4}$

$\Rightarrow \text{a}=\text{Percenatge increased}$
$\text{a}=\frac{1}{4}\times 100=0.25\times 100=25\%$

Step 2: Solving for b
Given, the number 5 is decreased by b% to reach 5.

$\text{5 is decreaded by b\% = 5 - 5}\text{b}\therefore 5+5\text{b}=45\text{b}=5-45\text{b}=1\text{b}=\frac{1}{5}$

$\Rightarrow \text{b}=\text{Percenatge decreased}$
$\text{b}=\frac{1}{5}\times 100=0.2\times 100=20\%$

$\therefore$a$=25\%,$b$=20\%$
Option a is correct: a > b