1. Did you find the bag?

-Yes, it was on your bed.

2. Where is that pen?
- It is under the bed.

3. Did you see my pencil case?
- Yes, it was next to the bookcase.
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It refers to 'the bag,' 'that pen,' and 'my pencil case' each. Is ther no problem in using 'the' in each sentence?

No problem at all. Each of them reads really well.

=)