In an elementary chemical reaction  $A\left(aq\right)\stackrel{t_{1/2}=10\min }{\to }2B\left(aq\right)+C\left(aq\right)$
Reaction mixture react with another reactant T and n-factor of A, B and C when react with T is in the ratio 2:1:2 respectively. The reaction started by taking ‘A’ only. If volume of ‘T’ used at 10 min is 40 ml. Volume of T used at t = 0 is x ml, at t = 20 min, is y ml and at $t=\infty iszml$  .
Find out the value of  $\frac{y+z}{x}\mathrm{......}?$
 

 $$\begin{gathered} A\left(aq\right)\underset{ }{\overset{ }{\to }}2B\left(aq\right)+C\left(aq\right) \\ t=0 a 0 0 \\ t=10\min a-\frac{a}{2} a\frac{a}{2} \\ t=20\min a-\frac{3a}{4} \frac{3a}{2} \frac{3a}{4} \\ t=\infty 0 2a a \end{gathered}$$
 Let the normality of ‘T’ is N and initial volume of ‘T’ is used x ml
At t=0 Meq. Of A=Meq. Of T
$a\times 2n=N\times x\mathrm{.........}\left(1\right)$ 
At t=10 min  Meq. Of  $(A+B+C)$   =Meq. Of T
 $\frac{a}{2}\times 2n+a\times n+\frac{a}{2}\times 2n=40\times N\mathrm{........}\left(2\right)$
At t=20 min  Meq. Of  $(A+B+C)$=Meq. Of T
 $\frac{a}{4}\times 2n+\frac{3a}{2}\times n+\frac{3a}{4}\times 2n=N\times y\mathrm{........}\left(3\right)$
At t=  $\infty$  min  Meq. Of  $(B+C)$ =Meq. Of T
 $2a\times n+a\times 2n=N\times z\mathrm{......}\left(4\right)$
Solving these equations,  $x=\frac{80}{3}ml,y=\frac{140}{3}ml,z=\frac{160}{3}ml$
Value of   $\frac{y+z}{x}=3.75$