A battery with finite internal resistance is connected across an external resistance. When the external resistance is increased to five times,  The voltage across the battery terminals increases from 10 V to 30 V.  The emf of the battery is

60V

Voltage across teminal of battery is $V = E -  Ir = E - \frac{E}{r+R} r = \frac{E}{R+r} R $

$\frac{E}{R+r} R = 10$  .............(1)

$\frac{E}{5R+r} 5R = 30$  .........(2)

Divide (2) and (1) 

$\Rightarrow \frac{5(R+r)}{5R+r} = 3$
$ \Rightarrow 5R + 5r = 15R + 3r $

$ \Rightarrow 10R = 2r , r = 5R$

From equation (1) , E = 60V