JSFiddle - React, Tailwind, and code Playground

HTML

<div class="dropdown">
    <select>
       <option value="">Some Text</option>
        <option value="">Some More Text2</option>
        <option value="">Some More More More Longer Text</option>
    </select>
                                
    </div>

CSS

.dropdown{
    width: 150px;
	border: 1px solid #cfcfcf;
	height: auto;
	border-radius: 5px;
	padding:3px 4px 4px;
	position: relative;
	z-index: 0;
	overflow:hidden;
	}

.dropdown select{
	border: none;
	background-color: transparent;
	outline: none;
	padding: 1px 0 0 5px;
	width:165%;
	background: url(http://i57.tinypic.com/nnmgpy_th.png) no-repeat right;
background-position: 55%;
    padding-right: 80%;
	}