The least fraction to be subtracted from the expression 31/4 - 4/5 of 5/641/3 ÷ 1/5 - ( 310 + 211/5 ) to make it an integer?

Answer: Option A

$$\begin{array}{rl}& \text{According to question,}\\ & \frac{3\frac{1}{4}-\frac{4}{5}\text{ of }\frac{5}{6}}{4\frac{1}{3}÷\frac{1}{5}-\left(\frac{3}{10}+21\frac{1}{5}\right)}\\ & \Rightarrow \frac{\frac{13}{4}-\frac{4}{5}\times \frac{5}{6}}{\frac{13}{3}\times 5-\left(\frac{3}{10}+\frac{106}{5}\right)}\\ & \Rightarrow \frac{\frac{13}{4}-\frac{2}{3}}{\frac{65}{3}-\frac{3}{10}-\frac{106}{5}}\\ & \Rightarrow \frac{\frac{39-8}{12}}{\frac{650-9-636}{30}}\\ & \Rightarrow \frac{31}{12}\times \frac{30}{5}\\ & \Rightarrow \frac{31}{2}\\ & \Rightarrow 15\frac{1}{2}\end{array}$$
∴ Least fraction number should be subtracted is:
$$\text{15}\frac{1}{2}-15=\frac{1}{2}$$     (least fraction number)