A liquid takes 10 minute to cool from 75℃ to 50℃ how much time will it take to cool from 60℃ to 40℃ temperature is surrounding is 20℃

Dear Amar
According to Newton's law of cooling, we have
mc (T₁ - T₂)/t = k [(T₁ + T₂)/2 - T₀)]  ---------------(1)
mc/k  =  [(T₁ + T₂)/2 - T₀)]/[(T₁ - T₂)/t]
mc/k = [(75+50)/2 - 20)]/[(75 - 50)/10]
     = 42.5 / 2.5 = 17
Substituting T₁ = 60 and T₂ = 40 and T0 = 20  (all in °C) in Eq. (1), we get
mc (60 - 40)/t = k [(60+ 40)/2   -  20)]
20 mc/t  = 30 k
t = 20 mc/(30k)
  = (20/30) * 17
  = 340/30 min
 = 11.33 min
The body takes 11.33 min to cool from 60°C to 40°C. 

Approved