Multiple choice

A juice maker makes juice of orange in soda (according to the customers' needs). Today, he made 54 l of 24% orange juice and kept it ready in a 54 l delivery container to be shipped to the customer. Just before delivery, he found out that the customer had asked for 54 l of 42% orange juice. To make what the customer wants, the juice maker replaced a portion of 24% juice by 78% juice. How much (in l) of 24% juice is replaced?

  1. 20 litres

  2. 16 litres

  3. 18 litres

  4. 14 litres

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

Let x be the amount of 24% juice replaced by 78% juice. 54 * 0.24 - x * 0.24 + x * 0.78 = 54 * 0.42. 12.96 + 0.54x = 22.68. 0.54x = 9.72. x = 18.

AI explanation

Using the replacement method, let x litres of the 24 percent juice be replaced by 78 percent juice. The equation for the final concentration is 24 percent of (54 - x) plus 78 percent of x equals 42 percent of 54. Solving (12.96 - 0.24x) + 0.78x = 22.68 gives 0.54x = 9.72, which means x = 18. The required amount replaced is 18 litres.

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