In the above question, the amount of salt in the tank at the moment of overflow is

Options

A. 20 lb
B. 50 lb
C. 30 lb
D. None of these

Answer

D

Explanation

`(dQ)/(dt)+2/(10+2t)Q=4`
This is a linear equation, It solution is `Q=(40t+4t^(2)+c)/(10+2t)`……….(1)
At `t=0, Q=a=0`. Substituting these values into equation (1), we find that c=0. We require Q at the moment of overflow which from part (a) is t=20. Thus,
`Q=(40(20)+4(20)^(2))/(10+2(20))=40 lb`