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

Answer: Option D

As A and B are fixed, C is any point on AB, so if AC is increases then CB decreases.
A________3 cm_________ C _____2 cm____B
Then, solution can be visualized as,
Increase in AC 6% = $$\frac{106\times 3}{100}=3.18\text{cm}\text{.}$$
Decrease in CB = 0.18 cm
% decrease = $$\frac{0.18}{2}\times 100=9\%$$

Alternatively,
AC = 3 Cm.
BC = 2 Cm.
Increase in AC by 6%, then
New, AC = 3 + 6% of 3 = 3 + 0.18 = 3.18 cm.
0.18 cm increase in AC means 0.18 cm decrease in BC as already mentioned AB as the fixed point.
So, % decrease in BC,
$$\begin{array}{rl}& =\frac{\text{Actual}\text{Decrease}\text{in}\text{BC}}{\text{Original BC}}\times 100\\ & =\frac{0.18}{2}\times 100=9\%\end{array}$$