APEDIA

The problem states that adding 50 litres leaves the tank 10% empty. This implies that the 50 litres currently occupy $100\% - 10\% = 90\%$ of the tank's total capacity.

Let the total capacity of the tank be V. We know that $90\%$ of V = 50 litres. We need to find the remaining volume to fill the tank, which is the $10\%$ that is empty.

Since 90% equates to 50 litres, 10% will equate to $50 \times (10 / 90) = 50 / 9$ litres.

$50 / 9 = 5.555\dots$ litres. Wait, let me re-read the options. Option 1 is 55.56. How can that be? If the tank is 10% empty, you need 10% more. $50/9 = 5.55$. The options are all in the 50s. Let me re-read the question very carefully. 'After 50 litres of petrol was poured into an empty storage tank, it was still 10% empty. How much petrol must be poured into the storage tank in order to fill it?' The question asks for the *amount needed to fill it*, which should be 5.55. But the options are 55.56, 51.33... Is there a typo in the OCR? Let's rethink. What if it was 10% FULL? Then 10% = 50L. To fill it, you need 90% = 450L. Not an option. What if it means 'it was still 10% *of the poured amount* empty'? No. What if the tank capacity is very large and the '10% empty' refers to something else? No, 'still 10% empty' means it is 90% full. Wait, look at the options again: 55.56. What is $500/9$? $55.555\dots$. How can $500/9$ be the answer? If $90\%$ is 50, then $100\%$ is $50 / 0.9 = 55.555\dots$. The total capacity of the tank is 55.56 litres. The question asks 'How much petrol... must be poured into the storage tank in order to fill it?'. It usually means 'How much total petrol is needed to fill the tank from empty'. Or it's a poorly phrased question meaning 'What is the full capacity'. The phrasing 'must be poured into the storage tank in order to fill it' usually means the *remaining* amount. If it meant total, it would say 'what is the capacity'. Given the options, it clearly meant the total capacity. Or wait. What if it was poured into an ALREADY PARTIALLY FULL tank? 'After 50 litres... was poured into an empty storage tank' - okay, it started empty. Therefore, total capacity = $50 / 0.9 = 55.55\dots$. Since 5.55 is not an option, the question meant 'What is the total amount of petrol the tank holds when full?' or it meant 'What must be poured into the *empty* tank to fill it'. The options make it unequivocally clear that total capacity is requested. I will write the explanation assuming they want the total capacity, but acknowledge the ambiguous phrasing.

Equating 90% of the capacity to 50 litres, the full 100% capacity is calculated as $500/9 \approx 55.56$ litres.