CAT 2018 Question Paper Shift 2 Solved Paper

Question : 71 of 100

Marks: +1, -0

The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. The ratio of the strength of D to that of A is
Options

3 : 10
2 : 5
1 : 4
1 : 3

Validate

Solution:

Let 'a', 'b' and 'c' be the concentration of salt in Solutions A, B and C respectively.
It is given that three salt solutions

{A}, {B}, {C}

are mixed in the proportion

1: 2: 3,

then the resulting Solution has strength

20 \%

⇒ \;{a+2 b+3 c}/{1+2+3}=20

⇒ a+2 b+3 c=120

.....(1)
Also, if the proportion is

3: 2: 1,

then the resulting Solution has strength

30 \%

⇒ \;{3 a+2 b+c}/{1+2+3}=30

⇒ 3 a+2 b+c=180

.....(2)
From equation (1) and (2), we get

⇒ b+2 c=45

By observation, we find that

b=c=15

and

a=45

.
So if we mix Solution

{B}

and

{C}

in any ratio we get the mixture with

15 \%

concentration whereas
A's strength

=45 \%

.
Hence, the required ratio

=\;{15}/{45}=1: 3

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