Multiple choice

A tin of oil was $\displaystyle \frac{4}{5}$ full. When 6 bottles of oil was taken out and 4 bottles of oil was poured into it it was $\displaystyle \frac{3}{4}$ full. How many bottles of oil can the tin contain?

  1. $10$
  2. $20$
  3. $30$
  4. $40$
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D Correct answer
Explanation

Let x be the total capacity. The change in volume is (4/5)x - 6 + 4 = (3/4)x. Solving for x: (4/5)x - (3/4)x = 2, which simplifies to (1/20)x = 2, so x = 40.

AI explanation

Let the total capacity of the tin be x bottles. The initial volume of oil is 4/5 of x, and the final volume after taking out 6 bottles and pouring in 4 is 3/4 of x. This gives the equation 4x/5 minus 2 equals 3x/4, since 6 minus 4 leaves a net loss of 2 bottles. Multiplying by 20 yields 16x minus 40 equals 15x, which results in x equals 40.

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