Let's start out with the ratio 4 : 5.

Let the number of pineapples at first be 4 units and the number of mangoes at first be 5 units. Now, we know that the ratio of the number of pineapples SOLD to the number of mangoes SOLD is 3 : 4, but these are not the same units as the 4 : 5 ratio. As such, we can't do much here.

However, we know that these number of pineapples sold corresponds to 2/3 of the original number of pineapples, or 2/3 of 4 units.

But 2/3 of 4 is not a whole number.

So, let's start the question all over and redefine our ratio 4 : 5 at the start by multiplying the ratio by 3 to make it 12 : 15.

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Let the number of pineapples at first be 12 units and the number of mangoes at first be 15 units.

The number of pineapples sold is 2/3 of 12 units, or a total of 8 units.

So now we know that 8 units of pineapples are sold.

Now, the ratio of pineapples sold to mangoes sold is 3 : 4. If 8 units of pineapples are sold, how many units of mangoes are sold?

Again, we are stuck here, so let's redefine our ratio at the start by multiplying the ratio by 3 to become 36 : 45.

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Let the number of pineapples at first be 36 units and the number of mangoes at first be 45 units.

The number of pineapples sold is 2/3 of 36 units, or a total of 24 units.

So now we know that 24 units of pineapples are sold.

Now, the ratio of pineapples sold to mangoes sold is 3 : 4. If 24 units of pineapples are sold, how many units of mangoes are sold?

From this, we can work out that a total of 32 units of mangoes are sold.

Since the starting number of mangoes is 45 units and the number of mangoes sold is 32 units, there must have been 13 units of mangoes remaining.

This corresponds to 52 mangoes.

13 units = 52
1 unit = 4

We need to find out the total number of fruits at the start, which is a total of 36 + 45 = 81 units.

81 units = 324

So, the number of fruits at the start must be 324.

This is amazingly clear, thank you so much for explaining. I am now more confident to do these kinds of questions. Thank you very much.