Question

A number is increased by 10$\%$ and then reduced by 10$\%$. After this operation, the number

• A. Does not change.
• B. Decreases by 1$\%$
• C. Increases by 1$\%$.
• D. Increases by 0.1$\%$

Answer 1

Answer: (B)

Decreases by 1$\%$

Answer 2

The correct option is (B): Decreases by 1$\%$
When a number $x$ is increased by $10\%$, the new value becomes:
$x + 0.1x = 1.1x$
Then, when this increased value is reduced by $10\%$:
$1.1x - 0.1(1.1x) = 1.1x - 0.11x = 0.99x$
This shows that after the operations, the final value is $0.99x$, which means the number decreases by $1\%$.
Thus, the correct answer is Option B: Decreases by 1%.