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)6\%
(b)7\%
(c)8\%
(d)9\%
Answer
Answer (as printed): D
Explanation
Original length of $\mathrm{AB}=5 \mathrm{cm}$. Original length of $\mathrm{AC}=3 \mathrm{cm}$. Original length of $\mathrm{CB}=(5-3) \mathrm{cm}=2 \mathrm{cm}$. New length of $\mathrm{AC}=106 \%$ of $3 \mathrm{cm}=\left(\frac{106}{100} \times 3\right) \mathrm{cm}=3.18 \mathrm{cm}$. New length of $\mathrm{CB}=(5-3.18) \mathrm{cm}=1.82 \mathrm{cm}$. Decrease in length of $\mathrm{CB}=(2-1.82) \mathrm{cm}=0.18 \mathrm{cm}$. $$\text { ∴ Decrease } \%=\left(\frac{0.18}{2} \times 100\right) \%=9 \% \text {. }$$