If a = b × dc ; b, c and d are increased by 10%, then by how much does a increase ?

Answer: Option A

$$\begin{array}{rl}& \text{Let,}\\ & B=110\%\text{ of }b=\frac{11b}{10}\\ & C=110\%\text{ of }c=\frac{11c}{10}\\ & D=110\%\text{ of }d=\frac{11d}{10}\\ & \text{Then,}\\ & A=B\times \frac{D}{C}\\ & A=\frac{11b}{10}\times \frac{11d}{10}\times \frac{10}{11c}\\ & A=\frac{11bd}{10c}\\ & A=\frac{11}{10}a\\ & A=\frac{110}{100}a\\ & A=110\%\text{ of }a\\ & \therefore \text{ Increase }\%=10\%\end{array}$$