Question

the ratio of spirit and water in a mixture is 1:8 the volume of the solution is increased by 25% adding spirit only. What is the resultant ratio of spirit and water?

Answer 1

Let the initial volume of water and spirit be $x$ and $8x$ respectively.

Total volume of the solution $\left(V\right)=x+8x=9x$

As the volume is increased by $25\%$.

Therefore,

New volume $\left(V^{\prime }\right)=9x+\frac{25}{100}\times 9x$

$\Rightarrow V^{\prime }=9x+\frac{9}{4}x=\frac{45}{4}x$

Since only spirit is added, i.e., volume of water is still $8x$.

Therefore,

Volume of spirit in the new solution $=\frac{45}{4}x-8x=\frac{13}{4}x$

Now,

Resultant ratio of spirit and water $=\frac{13}{4}x:8x=13:32$.

Hence the resultant ratio of spirit and water is $13:32$.