velocity of belt:

velocity of belt passing over the driver pulley will decrease

Now with this velocity belt pass over driven pulley, Now

Velocity of Driven = Velocity of Belt - Velocity of belt X (S2  /100)

But velocity of driven 
Equate equation (iii) and (iv)

N₂D₂  = N₁D₁(1-s₁/100-s₂/100 + s₁.s₂/10,000)

= N₁D₁[1-(s₁+s₂)/100], By neglecting s₁.s₂/10,000, since very small

If  s₁ + s₂= S = Total slip in %

N₂/N₁  = D₁/D₂[1-S/100]

This formula is used when total slip in percentage is given in problem

NOTE: If Slip and thickness are given then, Velocity ratio can be given by,

V.R = N₂/N₁  =  [1-s/100]