Sunil can do a piece of work in 10 days and Nikhil alone can do it in 12 days. Nikhil works it for 3 days and then leaves. Sunil alone can finish the remaining work in   

Work done by Sunil  in 1 day $=\frac{100\%}{10}\Rightarrow 10\%$

Work done by Nikhil  in 1 day $=\frac{100\%}{12}\Rightarrow \frac{25}{3}\%$

Work done by Nikhil  in 1 day $=\frac{100\%}{12}\Rightarrow \frac{25}{3}\%$

Work done by Sunil  in 3 days $=\frac{25}{3}\times 3\Rightarrow 25\%$

$75\%$ of  work done by Sunil $=75\times \frac{1}{10}=7.5days$

Or 

Sunil's one day work = $\frac{1}{10}$

Nikhil's one day work = $\frac{1}{12}$

Nikhil's 3 days work = $\frac{3}{12}=\frac{1}{4}$

Remaining work ( $\frac{3}{4}th$) can finish by Sunil in 

$1\to \frac{1}{10}$

$$\begin{gathered} ?\to \frac{3}{4} \\ \Rightarrow 7.5 days \end{gathered}$$