Mongodb condition check array is not work as I expect

I have the following BSON :

[
  {
    arr: [
      {
        age: 24
      },
      {
        age: 55
      }
    ]
  },
  {
    arr: [
      {
        age: 12
      },
      {
        age: 14
      },
      {
        age: 17
      }
    ]
  },
  {
    arr: [
      {
        age: 11
      },
      {
        age: 13
      },
      {
        age: 20
      }
    ]
  }
]

I use the below query :

db.collection.find({
  "arr": {
    $elemMatch: {
      age: {
        $lt: 15
      }
    }
  }
},
{
  "arr.$": 1
})

and the result is :

[
  {
    "_id": ObjectId("5a934e000102030405000001"),
    "arr": [
      {
        "age": 12
      }
    ]
  },
  {
    "_id": ObjectId("5a934e000102030405000002"),
    "arr": [
      {
        "age": 11
      }
    ]
  }
]

My challenge is that I want if all the elements inside each arr array are less than 15 the it returns them and not when one of them are less than 15. So in this case my expectation answeris an empty array as the output as not all the elements of each array has the age value under 15. I am not sure if I need to use $elemMatch in this case. If there is an alternative to do it please let me know. I just want to get the solution as the query result rather than javascript manipulations on the post processing. By the way I used https://mongoplayground.net/ to check the dataset.

Perhaps you need

when you

When you take the extra mile to

you should share the playground link, it makes answering easier.