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CAT 2017 Slot 2 — QA Question 14

MixturesEasy

Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B and C respectively, are further mixed in the proportion 4 : 3 : 2. Then the resulting mixture has

Answer & solution

Correct answer: More water than liquid B

  • A

    The same amount of water and liquid B

  • B

    The same amount of liquids B and C

  • More water than liquid B

  • D

    More water than liquid A

Solution

Easy

Each mixture splits into a known water fraction. Pick a convenient common volume so all amounts are whole numbers, total the water and each liquid, then compare. Only one inequality among the options holds.

1

Water fraction of each mixture. Water : liquid ratios 1:2, 1:3, 1:41{:}2,\ 1{:}3,\ 1{:}4 give water fractions over totals 3,4,53,4,5.

water in M1=13,water in M2=14,water in M3=15\begin{aligned} &\text{water in M1} = \tfrac13,\quad \text{water in M2} = \tfrac14,\quad \text{water in M3} = \tfrac15 \end{aligned}
2

Choose volumes. The mixtures are combined as 4:3:24:3:2. Scaling by 6060 (a multiple of 3,4,53,4,5) keeps every part whole.

M1=4×60=240,M2=3×60=180,M3=2×60=120\begin{aligned} &M1 = 4\times 60 = 240,\quad M2 = 3\times 60 = 180,\quad M3 = 2\times 60 = 120 \end{aligned}
3

Total water. Apply the water fraction to each volume and add.

water=13(240)+14(180)+15(120)⇒ =80+45+24=149\begin{aligned} &\text{water} = \tfrac13(240) + \tfrac14(180) + \tfrac15(120)\\ &\Rightarrow\ = 80 + 45 + 24 = 149 \end{aligned}
4

Liquid B. B is only in mixture M2, where it is 34\tfrac34 of the volume.

liquid B=34×180=135\begin{aligned} &\text{liquid B} = \tfrac34\times 180 = 135 \end{aligned}
5

Compare. Water =149=149 exceeds liquid B =135=135. (Liquid A =23×240=160=\tfrac23\times 240 = 160, liquid C =45×120=96=\tfrac45\times120 = 96, so the other options fail.)

149>135(water > liquid B)\begin{aligned} &149 > 135 \quad\text{(water } > \text{ liquid B)} \end{aligned}
More water than liquid B\textbf{More water than liquid B}

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CAT 2017 Slot 2 QA Q14: Consider three mixtures – the first having water and liquid A in the ratio 1 : 2, the second having wate — Solution | TheCATExam