A lens of focal length 20 cm forms the image of a bright object kept 30 cm from it on a screen. If the lens is replaced by another lens, the object has to be moved by 5 cm to obtain a sharp image on the screen. Find the possible values of the focal length of the second lens.

u₁ = 20cm

f₁ = 15cm

therefore 1/v₁ = 1/u₁ + 1/f₁

1/v₁ = 1/20 + 1/15

1/v₁ = 7/60

v₁ = 60/7

now object is shifted 

two cases arise 1)- object moved away from second lens 2)- object is moved towards the lens

v₂ = 60/7

u₂ = 35 , 25

therefore the two possible focal lenghts will come out as 420/37cm  and 300/23cm respectively.