A number is increased by 10 percent. Then it is decreased by 20 percent. If the final value of number is 528, then what is the initial value of number?

Correct option is D

Given:
Increase in number = 10%
Decrease in number = 20%
Solution:
Let the number be 100x.
After 10% is increased,
New number = 100x × 100x + 10% = 110x
After 20% decreased,
New number = 110x - 110x × 20% = 110x - 22x = 88x
Given that
88x = 528
=> x =6
So, 100x = 600
∴ The initial value of the number is 600.
Alternate Solution:
Let the initial number be 100%.
​$$\text{Overall Percentage Change} = a\% + b\% + \frac{ab}{100}\% \Rightarrow 10\% + (-20\%) + \frac{10 \times (-20)}{100}\% \Rightarrow -10\% - 2\% \Rightarrow -12\%$$​​
100% - 12% = 528
=> 88% = 528
=> 1% = 6
=> 100% = 600
∴ The initial value of the number is 600.