One cup has juice and water in the ratio 5 : 2, while another cup of the same capacity has them in the ratio 7 : 4, respectively. If contents of both the cups (when full) are poured in a vessel, then what will be the final ratio of water to juice in the vessel?

Solution(By Examveda Team)

\[\begin{array}{*{20}{c}} {}&{{\text{Juice}}}&:&{{\text{Water}}}&{{\text{Total}}} \\ {{{\text{I}}^{{\text{st}}}}}&{{5_{ \times 11}}}&:&{{2_{ \times 11}}}&{{7_{ \times 11}}} \\ {{\text{I}}{{\text{I}}^{{\text{nd}}}}}&{{7_{ \times 7}}}&:&{{4_{ \times 7}}}&{{{11}_{ \times 7}}} \end{array}\]
Capacity of both cup is same
\[\begin{array}{*{20}{c}} {}&{{\text{Juice :}}\,{\text{Water}}\,\,\,{\text{Total}}} \\ {{{\text{I}}^{{\text{st}}}}}&{55\,\,\,:\,\,\,22\,\,\,\,\,\,\,\,\,\,77} \\ {{\text{I}}{{\text{I}}^{{\text{nd}}}}}&{49\,\,\,:\,\,\,28\,\,\,\,\,\,\,\,\,\,77} \\ {{\text{Total}}}&{\overline {\underline {\,104\,\,:\,\,50\,\,\,\,\,\,\,\,\,154\,} } } \end{array}\]
Final ratio of water to juice in cup = 50 : 104 = 25 : 52