Question

A long sighted person has a minimum distance of distinct vision 50cm .he wants to reduce to 25cm .He should use what type of lens and focal length

Answer 1

He should use concave lens. 
P = 100/f(in cm)
   = 100/50
   = 2 D

1/f = 1/v - 1/u
1/f = -1/50 - (-1/25)
1/f = -1/50 + (1/25)
1/f = (-1 +2)/50
1/f = 1/50
f = 50cm or 0.5m

Answer 2

A long sighted person means that he can see distant object clearly but he cannot see objects near to him .This defect is also known as Hypermetropia.

Given : 
v=-50cm
u=-25cm(normal near point)
focal length=?
Lens formula:
1/f=1/v-1/u
1/f=1/-50 -1/-25
=1/25-1/50
=2-1/50=1/50
f=50cm
Hence convex lens of focal length 50cm should be advised or used to correct this defect.