If p : q = 3 : 4, r : s = 8 : 5 and x : y = 10 : 6, then psx : qry is equal to.

1¹⁶/₂₅
2²⁵/₃₂
32
4⁷⁵/₃₂

Answer:- 1

Explanation:-

Solution:

\begin{aligned} = \frac{p}{q} = \frac{3}{4}, \frac{r}{s} = \frac{8}{5}, \frac{x}{y} = \frac{10}{6} \\ \Rightarrow p = \frac{3 q}{4}, r = \frac{8 s}{5}, x = \frac{5 y}{3} . \\ ∴ \frac{p s x}{q r y} = \frac{\frac{3 q}{4} \times s \times \frac{5 y}{3}}{q \times \frac{8 s}{5} \times y} \\ = \frac{\frac{5}{4} q s y}{\frac{8}{5} q s y} \\ = \frac{5}{4} \times \frac{5}{8} \\ = \frac{25}{32} . \end{aligned}

$\eqalign{ & = \frac{p}{q} = \frac{3}{4},\frac{r}{s} = \frac{8}{5},\frac{x}{y} = \frac{{10}}{6} \cr & \Rightarrow p = \frac{{3q}}{4},r = \frac{{8s}}{5},x = \frac{{5y}}{3}. \cr & \therefore \frac{{psx}}{{qry}} = \frac{{\frac{{3q}}{4} \times s \times \frac{{5y}}{3}}}{{q \times \frac{{8s}}{5} \times y}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{\frac{5}{4}qsy}}{{\frac{8}{5}qsy}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{5}{4} \times \frac{5}{8} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{25}}{{32}}. \cr}$