zones = [{
    zone: 'A',
    price: '20'
  },
  {
    zone: 'B',
    price: '20'
  },
  {
    zone: 'C',
    price: '20'
  }
];

var result = []

for (let i = 0; i < zones.length; i++) {
  for (let k = 1; k < zones.length; k++) {
    if (zones[i].zone === zones[k].zone && i != k && result.indexOf(zones[i].zone) == -1) {
      result.push(zones[i].zone)
      console.log(zones[i].zone)
    }
  }
}

found this answer here : post 1

 var zones = [
    {zone:'A' : price:'20'},
    {zone:'B' : price:'20'},
    {zone:'C' : price:'20'},
    {zone:'A' : price:'20'},
 ];

 unique = [...new Set(zones.map(propYoureChecking => 
    propYoureChecking.zone))];
    if (unique.length === 1) {
    console.log(unique);
 }

and for normal arrays : post 2

You can do it a few different ways: here's one (from the post):

 const arry = [1, 2, 1, 3, 4, 3, 5];

 const toFindDuplicates = arry => arry.filter((item, index) => arr.indexOf(item) !== index)
 const duplicateElementa = tofindDuplicates(arry);
 onsole.log(duplicateElements);

// Output: [1, 3]

Your requirement is a bit vague but assuming you want to find the index of the duplicate object(s).

zones = [
{zone:'A', price:'20'},
{zone:'B', price:'20'},
{zone:'C', price:'20'},
{zone:'A', price:'20'},
];

const zoneAIndices = [];

zones.forEach((zone, index) => {
 if( zone.zone === 'A') {
   zoneAIndices.push(index);
 }
});

Now zoneAIndices[1] has the index of the duplicate item.

Note:

the zones array you have defined is incorrect, instead of : between zone and price it should be a ,