Multiple choice

'n' litres of oil was poured into a tank and it was still e% empty. How much oil must be poured into the tank in order to fill it to the brim?

  1. $\displaystyle \frac{ne}{100+e}$
  2. $\displaystyle \frac{100-e}{ne}$
  3. $\displaystyle \frac{ne}{100-e}$
  4. $\displaystyle \frac{100+e}{ne}$
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C Correct answer
Explanation

If the tank is e% empty, it is (100-e)% full. The current volume n represents (100-e)/100 of the total capacity T, so T = 100n / (100-e). The amount needed to fill the remaining e% is (e/100) * T, which simplifies to (e/100) * (100n / (100-e)) = ne / (100-e).

AI explanation

If the tank is e% empty after pouring in n litres, the current volume represents (100 - e)% of the total capacity of the tank. The total capacity V is found by V = (n * 100) / (100 - e). The additional amount of oil needed to fill the tank is V - n, which simplifies to [100n / (100 - e)] - [n(100 - e) / (100 - e)], yielding ne / (100 - e).

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