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A 60% spirit solution is mixed with r% spirit solution in the ratio 1 : 3 such that a s% spirit solution is obtained. When a (s/3)% spirit solution is mixed with 55% spirit solution in equal ratio, an (r/2)% spirit solution is obtained. Which of the following can be determined? (A) Value of ‘r’ (B) Value of ‘s’ (C) Volume of the 60% spirit solution mixed initially (D) If 9 liters of r% spirit solution was mixed initially, what was the volume of the s% spirit solution thus obtained?

A 60% spirit solution is mixed with r% spirit solution in the ratio 1 : 3 such that a s% spirit solution is obtained. When a (s/3)% spirit solution is mixed with 55% spirit solution in equal ratio, an (r/2)% spirit solution is obtained. Which of the following can be determined? (A) Value of ‘r’ (B) Value of ‘s’ (C) Volume of the 60% spirit solution mixed initially (D) If 9 liters of r% spirit solution was mixed initially, what was the volume of the s% spirit solution thus obtained? Correct Answer Only A, B and D

By allegation method:

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∴ (r - s)/(s – 60) = 1/3

⇒ s – 60 = 3r – 3s

⇒ 4s – 3r = 60     ----(i)

Also, ((s/3) + 55)/2 = r/2

⇒ s/3 + 55 = r

⇒ 3r – s = 165     ----(ii)

(i) + (ii) gives,

3s = 225

⇒ s = 75

∴ r = (4 × 75 – 60)/3 + 80

So, (A) and (B) can be determine.

(C) cannot be determined as only ratios are given, the volumes of each type of solution mixed is not provided.

(D) : Volume of 60% spirit solution mixed initially = 3 + 9 = 12 liters.

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