Multiple choice

A jar is filled with a mixture of two liquids $A$ and $B$ in the proportion $A:B:: 5:3,$ when $16$ litres of the mixture is drawn off and the jar is filled with liquid $B,$ then the proportion becomes $A:B::3:5.$ How many litres of mixture does the jar hold?

  1. $35$ $L$
  2. $50$ $L$
  3. $45$ $L$
  4. $40$ $L$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the jar hold 8x total. A = 5x, B = 3x. Removing 16L removes 10L of A and 6L of B. Remaining: A = 5x - 10, B = 3x - 6 + 16 = 3x + 10. Ratio (5x-10)/(3x+10) = 3/5. 25x - 50 = 9x + 30, 16x = 80, x = 5. Total = 8x = 40L.

AI explanation

Let the total capacity of the jar be x liters. The amount of liquid A left after removing 16 liters and replacing it with liquid B is given by 5 eighths of x, which makes the new ratio of A to the total mixture 3 divided by 8. Setting 5x divided by 8 equal to 3 divided by 8 multiplied by x gives 5x equals 3x plus 48. Solving this equation shows the jar holds 40 L.

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