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CAT 2024 Slot 2 — QA Question 7

MixturesEasy

A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

Answer & solution

  • A

    4 : 5

  • B

    5 : 3

  • C

    5 : 4

  • 3 : 5

Solution

Easy

Let the original solution have aa litres acid and ww litres water. Translate each concentration statement into one equation, solve, then report the original water-to-acid ratio.

1

After adding 2 L water, acid is 50%. Acid stays aa, water becomes w+2w+2; equal halves means acid = water.

a=w+2(50% acid ⇒ acid = water)\begin{aligned} &a=w+2 \quad\text{(50\% acid }\Rightarrow\text{ acid = water)} \end{aligned}
2

After adding 15 L acid, acid is 80%. Acid =a+15=a+15, total =a+15+w+2=a+15+w+2.

a+15=0.8 (a+w+17)⇒ a+15=0.8 (2a+15)(put w=a−2 from step 1)⇒ a+15=1.6a+12⇒ 3=0.6a ⇒ a=5\begin{aligned} &a+15=0.8\,(a+w+17)\\ &\Rightarrow\ a+15=0.8\,(2a+15) \quad\text{(put }w=a-2\text{ from step 1)}\\ &\Rightarrow\ a+15=1.6a+12\\ &\Rightarrow\ 3=0.6a\ \Rightarrow\ a=5 \end{aligned}
3

Recover water and form the ratio. From step 1, w=a−2=3w=a-2=3.

water:acid=w:a=3:5\begin{aligned} &\text{water}:\text{acid}=w:a=3:5 \end{aligned}
water:acid=3:5\text{water}:\text{acid}=3:5
CAT 2024 Slot 2 QA Q7: A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, t — Solution | TheCATExam