Multiple choice

Two batches of drinks are prepared by using mixture of Vodka and Juice. In the first batch, the ratio of Vodka and Juice is 1 : 2 and in second batch, the ratio is 2 : 3. In what ratio should these two batches be mixed, so that we can get a new batch of Juice and Vodka in the ratio 5 : 3?

  1. 7 : 4

  2. 5 : 3

  3. 4 : 5

  4. 3 : 5

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Batch 1: V:J = 1:2 (V=1/3). Batch 2: V:J = 2:3 (V=2/5). Target: J:V = 5:3 (V=3/8). Use alligation on V: 1/3 and 2/5 to get 3/8. |2/5 - 3/8| = 1/40. |1/3 - 3/8| = 1/24. Ratio = (1/40) : (1/24) = 24:40 = 3:5.

AI explanation

By the method of alligation, compare the required Vodka concentration of 3/8 to the given batches. The first batch has a Vodka concentration of 1/3 and the second batch has a concentration of 2/5. The ratio of their quantities is (2/5 - 3/8) : (3/8 - 1/3), which equals 1/40 : 1/24. Multiplying both sides by 120 yields the mixing ratio of 3 : 5.

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