Multiple choice

Vessels P and Q contain mixtures of fruit juice and soda in the ratios 3 : 7 and 5 : 2, respectively. In what ratio should the quantities of mixture be taken from vessels P and Q to form a mixture in which the ratio of fruit juice to soda is 5 : 3?

  1. 5 : 11

  2. 25 : 91

  3. 91 : 25

  4. 15 : 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using alligation on fruit juice: P has 3/10, Q has 5/7. Target is 5/8. |5/7 - 5/8| = 5/56. |3/10 - 5/8| = |12/40 - 25/40| = 13/40. Ratio = (5/56) : (13/40) = (5/7) : (13/5) = 25 : 91.

AI explanation

Using the rule of alligation on the fruit juice percentages of the two vessels gives the required mixing ratio. The fraction of fruit juice in vessel P is 3/10 (30%) and in vessel Q is 5/7 (about 71.4%), while the desired mixture has a 5/8 fraction (62.5%). The alligation calculation results in a ratio of (5/7 - 5/8):(5/8 - 3/10), which simplifies to 25:91.

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