If E gave C 21 pears, their ratio C : E is 3 : 1

Let the new number of C's pears be 3 units.
Then the new number of E's pears is 1 unit.

This means that C must have had (3 units - 21) pears at first, while E must have had (1 unit + 21) pears at first.

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If C gave E 12 pears, their ratio C : E is 3 : 2

Let the new number of C's pears be 3 parts. We cannot use units as the scenario is different, but the "parts" idea is similar to the "units" idea, just a different name for it.
Then the new number of E's pears is 2 parts.

This means that C must have had (3 parts + 12) pears at first, while E must have had (2 parts -12) pears at first.

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So at first, we can say that

C had (3 units - 21) pears or (3 parts + 12) pears at first. These represent the same number of pears, so

3 units - 21 = 3 parts + 12

Similarly, E had (1 unit + 21) pears or (2 parts - 12) pears at first. These represent the same number of pears, so

1 unit + 21 = 2 parts - 12

Let's piece these up together.

(Celia) 3 units - 21 = 3 parts + 12
--> 3 units = 3 parts + 33
Since 3 parts + 33 can be classified as 3 groups of (1 part + 11),
--> 1 unit = 1 part + 11

(Eliot) 1 unit + 21 = 2 parts - 12
--> 1 unit = 2 parts - 33

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But all the "units" represent the same number. Since 1 unit = 1 part + 11, but the same 1 unit = 2 parts - 33, we have

1 part + 11 = 2 parts - 33
11 = 2 parts - 33 - 1 part
11 = 1 part - 33
11 + 33 = 1 part
44 = 1 part
So, 1 part represents 44 pears.

1 unit = 1 part + 11 = 55
So, 1 unit represents 55 pears.

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Celia's number of pears at first
= 3 units - 21
= 3 * 55 - 21
= 165 - 21
= 144

Eliot's number of pears at first
= 1 unit + 21
= 55 + 21
= 76

Difference in pears
= 144 - 76
= 68

so Celia has 76 pears more than Eliot.

TQ