Question

A and B are two fixed points 5 cm apart and C is a point on AB, such that AC is 3 cm. If the length of AC is increased by 6$\%$, the length of CB is decreased by:

• A. $8\%$
• B. $6\%$
• C. $7\%$
• D. $9\%$

Answer 1

Answer: (D)

Given that, $AB=5cm$ and $AC=3cm$.

The length of $AC$ is increased by $6\%$.

To find out: The percentage by which the length of $BC$ will decrease.

We have, $AB=5cm$ and $AC=3cm$

$\therefore BC=5-3=2cm$

If $AC$ is increased by $6\%$, its length will become,

$AC+6\%ofAC=3+\frac{6}{100}\times 3$

$\therefore AC=3.18cm$

Now, $BC=AB-AC$

$\Rightarrow BC=5-3.18=1.82cm$

Hence, decrease in length of $BC=2-1.82cm=0.18cm$

$\therefore \%decrease=\frac{0.18}{2}\times 100$

$\Rightarrow 9\%$

Hence, the $BC$ will decrease by $9\%$.