Multiple choice

At a manufacturing unit, there is a container containing a mixture of rose essence and alcohol in the ratio of 5 : 3. If 15 litres of alcohol is added to the container, the ratio of rose essence to alcohol becomes 7 : 5. What was the initial amount of the mixture in the container?

  1. 185 litres

  2. 190 litres

  3. 210 litres

  4. 230 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let rose essence be 5x and alcohol be 3x. Total = 8x. Adding 15L alcohol: 5x / (3x + 15) = 7/5. 25x = 21x + 105, so 4x = 105, x = 26.25. Initial mixture = 8x = 8 * 26.25 = 210.

AI explanation

Let the initial quantities of rose essence and alcohol be 5x and 3x, respectively. When 15 litres of alcohol is added, the new ratio of rose essence to alcohol becomes 5x to 3x plus 15. The problem states this new ratio is 7 to 5, so we can set up the proportion 5x divided by (3x plus 15) equals 7 divided by 5. Solving this equation gives 25x equals 21x plus 105, meaning 4x equals 105. The initial amount of the mixture is 8x, which equals 8 multiplied by 26.25, resulting in 210 litres.

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