A person can see objects clearly only when they lie between $50$ cm and $400$ cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be:

The near point of a hypermetropic person is $75~\text{cm}$ from the eye. What is the power of the lens required to enable the person to read clearly a book held at $25~\text{cm}$ from the eye?
1. $+2.67~\text{D}$ 
2. $-1.25~\text{D}$ 
3. $-2.67~\text{D}$
4. $+1.25~\text{D}$