Question

Three containers have their volumes in the ratio 3: 4 : 5. They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of (4: 1), (3 : 1) and (5 : 2) respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is

• A. 4 : 1
• B. 151 : 48
• C. 157 : 53
• D. 5 : 2

Answer 1

The correct option is C 157 : 53

Suppose the ratio of three container $=3x,4xand5x$
Ratio of milk and water $=4a,a,3b,band5c,2c$ respectively
then
$4a+a=3x\therefore a=\frac{3}{5}x$
$3b+b=4x\therefore b=x$
$5c+2c=5x\therefore c=\frac{5}{7}x$
$\therefore amountofmilkinfourthcontainer=4\times \frac{3}{5}x+3x+5\times \frac{5}{7}x$
$\Rightarrow \frac{12}{5}x+3x+\frac{25}{7}x=\frac{314}{35}x$
Similarly amount of water in the fourth container $=\frac{3}{5}x+x+2\times \frac{5}{7}x=\frac{106}{35}x$
$\therefore RequiredRatio=\frac{314}{106}=\frac{157}{53}=157:53$