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CAT 2019 Slot 2 — QA Question 30

MixturesEasy

The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. Each of three vessels A, B, C contains 500 ml of salt solution of strengths 10%, 22%, and 32%, respectively. Now, 100 ml of the solution in vessel A is transferred to vessel B. Then, 100 ml of the solution in vessel B is transferred to vessel C. Finally, 100 ml of the solution in vessel C is transferred to vessel A. The strength, in percentage, of the resulting solution in vessel A is

Answer & solution

Correct answer: 14

  • A

    15

  • B

    12

  • C

    13

  • 14

Solution

Easy

Track the grams of salt (not the percentage) through the three transfers. Each 100100 ml poured carries a known fraction of the current salt. The final strength is salt in A divided by its 500500 ml volume.

Start (each 500500 ml): salt in A=50A=50 g (10%10\%), B=110B=110 g (22%22\%), C=160C=160 g (32%32\%).

1

A →\to B (100 ml of A's 500 ml). This carries 15\tfrac{1}{5} of A's salt =10=10 g.

salt A=50−10=40 g,VA=400 mlsalt B=110+10=120 g,VB=600 ml\begin{aligned} &\text{salt }A = 50-10 = 40\ \text{g},\quad V_A = 400\ \text{ml}\\ &\text{salt }B = 110+10 = 120\ \text{g},\quad V_B = 600\ \text{ml} \end{aligned}
2

B →\to C (100 ml of B's 600 ml). This carries 16\tfrac{1}{6} of B's salt =20=20 g.

salt B=120−20=100 g,VB=500 mlsalt C=160+20=180 g,VC=600 ml\begin{aligned} &\text{salt }B = 120-20 = 100\ \text{g},\quad V_B = 500\ \text{ml}\\ &\text{salt }C = 160+20 = 180\ \text{g},\quad V_C = 600\ \text{ml} \end{aligned}
3

C →\to A (100 ml of C's 600 ml). This carries 16\tfrac{1}{6} of C's salt =30=30 g.

salt A=40+30=70 g,VA=500 ml\begin{aligned} &\text{salt }A = 40+30 = 70\ \text{g},\quad V_A = 500\ \text{ml} \end{aligned}
4

Strength of A. 100100 ml holds 705=14\tfrac{70}{5}=14 g, i.e. 14%14\%.

strengthA=70500×100=14%\begin{aligned} &\text{strength}_A = \frac{70}{500}\times 100 = 14\% \end{aligned}
Strength of A=14%\text{Strength of A}=14\%

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CAT 2019 Slot 2 QA Q30: The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. Each of three vessel — Solution | TheCATExam