TheCATExam
Sign in

CAT 2017 Slot 2 — QA Question 3

AlligationEasy

Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water in 9 : 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3 : 1 ratio?

Answer & solution

Correct answer: 27 : 13

  • A

    27 : 14

  • 27 : 13

  • C

    27 : 16

  • D

    27 : 18

Solution

Easy

Track the milk fraction of each bottle and of the target mixture, then apply alligation: the mixing ratio is the inverse ratio of the distances of the two milk fractions from the target.

1

Milk fractions. Convert each ratio to the fraction that is milk.

Bottle 1: 77+2=79Bottle 2: 99+4=913Target: 33+1=34\begin{aligned} &\text{Bottle 1: }\frac{7}{7+2}=\frac{7}{9}\\ &\text{Bottle 2: }\frac{9}{9+4}=\frac{9}{13}\\ &\text{Target: }\frac{3}{3+1}=\frac{3}{4} \end{aligned}
2

Alligation distances. The ratio of volumes equals (target −- weaker) : (stronger −- target), where Bottle 1 (79\tfrac79) is the stronger milk source and Bottle 2 (913\tfrac{9}{13}) the weaker.

V1V2=34−91379−34⇒ 34−913=39−3652=352(top)⇒ 79−34=28−2736=136(bottom)\begin{aligned} &\frac{V_1}{V_2}=\frac{\frac34-\frac{9}{13}}{\frac79-\frac34}\\ &\Rightarrow\ \frac34-\frac{9}{13}=\frac{39-36}{52}=\frac{3}{52} \quad\text{(top)}\\ &\Rightarrow\ \frac79-\frac34=\frac{28-27}{36}=\frac{1}{36} \quad\text{(bottom)} \end{aligned}
3

Simplify the ratio. Divide the two fractions from step 2.

V1V2=352÷136=352×36=10852=2713⇒ V1:V2=27:13\begin{aligned} &\frac{V_1}{V_2}=\frac{3}{52}\div\frac{1}{36}=\frac{3}{52}\times 36=\frac{108}{52}=\frac{27}{13}\\ &\Rightarrow\ V_1:V_2=27:13 \end{aligned}
V1:V2=27:13V_1:V_2=27:13

Related Alligation questions

See all Mixture, Alligation, Removal & Replacement questions →
CAT 2017 Slot 2 QA Q3: Bottle 1 contains a mixture of milk and water in 7 : 2 ratio and Bottle 2 contains a mixture of milk and water — Solution | TheCATExam