Discussion

Explanation:

Proportion of wine in 3 samples is $\frac{1}{3}, \frac{2}{5}, \frac{3}{8}$

Proportion of water in 3 samples is $\frac{2}{3}, \frac{3}{5}, \frac{5}{8}$

Since equal quantities are taken, let 1 liter of each is mixed.

Total quantity of wine is $\frac{1}{3}+\frac{2}{5}+\frac{3}{8}$ = $\frac{133}{120}$

Total quantity of water is $\frac{2}{3}+\frac{3}{5}+\frac{5}{8}$ = $\frac{227}{120}$

∴ Proportion of wine and water in the solution is = 133 : 227.

Alternately,

Proportion of wine in 3 samples is $\frac{1}{3}, \frac{2}{5}, \frac{3}{8}$

Proportion of water in 3 samples is $\frac{2}{3}, \frac{3}{5}, \frac{5}{8}$

Since equal quantities are taken, let 120 liter of each is mixed.  (We’ve chosen 120 liters since it is divisible by the denominators of all the fractions i.e. LCM(3, 5 and 8) = 120)

Total quantity of wine is $\frac{1}{3}\times 120+\frac{2}{5}\times 120+\frac{3}{8}\times 120$ = 40 + 48 + 45 = 133.

Total quantity of water is $\frac{2}{3}\times 120+\frac{3}{5}\times 120+\frac{5}{8}\times 120$ = 80 + 72 + 75 = 227.

∴ Proportion of wine and water in the solution is = 133 : 227.

Hence, option (d).

» Your doubt will be displayed only after approval.