Multiple choice

In a mixture of juice, 22% is water and the remaining is juice. After removing and replacing 8 litres of the mixture with 8 litres of pure juice, the percentage of juice in the mixture increases to 81%. What was the original quantity of the mixture?

  1. 63 litres

  2. 91.67 litres

  3. 117 litres

  4. 58.67 litres

  5. a
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial mixture be X. Juice is 78% of X. Removing 8L removes 0.78*8 = 6.24L of juice. Adding 8L of pure juice adds 8L. New juice amount = 0.78X - 6.24 + 8 = 0.78X + 1.76. New concentration = (0.78X + 1.76)/X = 0.81. 0.78X + 1.76 = 0.81X, so 0.03X = 1.76, X = 58.67.

AI explanation

By the equation for replacement, the final quantity of water is given by W = Initial_W * (1 - Replaced/Total). The initial mixture has 22% water, and after replacing 8 litres with pure juice, the water becomes 19% of the total. This gives 0.19 * Total = 0.22 * (Total - 8), which simplifies to 0.03 * Total = 1.76. Solving this yields a total original quantity of 58.67 litres.

Keep practicing — related questions