CAT 2017 Slot 2 — QA Question 3

Bottle 1 contains 7/9 of milk
Bottle 1 contains 9/13 of milk

The final mixture contains 3/4 of milk

Now using the allegation rule, we get the ratio of quanities in bottles as:

⇒ $\frac{\mathrm{Quantity} \mathrm{in} \mathrm{bottle} 1}{\mathrm{Quantity} \mathrm{in} \mathrm{bottle} 2}$ = $\frac{{\displaystyle \frac{3}{4}}-{\displaystyle \frac{9}{13}}}{{\displaystyle \frac{7}{9}}-{\displaystyle \frac{3}{4}}}=\frac{{\displaystyle \frac{3}{52}}}{{\displaystyle \frac{1}{36}}}$

⇒ $\frac{\mathrm{Quantity} \mathrm{in} \mathrm{bottle} 1}{\mathrm{Quantity} \mathrm{in} \mathrm{bottle} 2}$ = $\frac{3}{52}÷\frac{1}{36}$ = $\frac{3}{52}\times \frac{36}{1}$ = $\frac{108}{52}$ = $\frac{27}{13}$ = 27 : 13

Hence, option (b).