Question

Three containers, A, B and C have the mixture of alcohol and water in the ratio 5 : 7, 7 : 2 and 3 : 5, respectively. If all the mixtures of all three vessels are poured into a single vessel, then the ratio of the total quantity of alcohol to water will be

• A. 107 : 105
• B. 103:105
• C. 111: 113
• D. 113 : 103
• E. None of the above

Answer 1

The correct option is D 113 : 103

Here, $a_1=5,b_1=7,$
$a_2=7,b_2=2,$
$a_3=3$
and $b_3=5$
By short Trick 1
Required ratio $=\frac{Totalquantityofalcohol}{Totalquantityofwater}$
$=\frac{\frac{a_1}{a_1+b_1}+\frac{a_2}{a_2+b_2}+\frac{a_3}{a_3+b_3}}{\frac{b_1}{a_1+b_1}+\frac{b_2}{a_2+b_2}+\frac{b_3}{a_3+b_3}}$
$=\frac{\frac{5}{5+7}+\frac{7}{7+2}+\frac{3}{3+5}}{\frac{7}{5+7}+\frac{2}{7+2}+\frac{5}{3+5}}=\frac{\frac{5}{12}+\frac{7}{9}+\frac{3}{8}}{\frac{7}{12}+\frac{2}{9}+\frac{5}{8}}=\frac{\frac{113}{72}}{\frac{103}{72}}=\frac{113}{103}=113:103$