demo, Sql Server - rextester

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--Sql Server 2014 Express Edition
--Batches are separated by 'go'

WITH yourTable AS (
    SELECT '2018-09-21 00:00:00.000' AS ROOMDATE, 129 AS rate, 346686 AS bus_id, 2 AS quantity UNION ALL
    SELECT '2018-09-21 00:00:00.000', 162, 354247, 36  UNION ALL
    SELECT '2018-09-21 00:00:00.000', 159, 382897, 150 UNION ALL
    SELECT '2018-09-21 00:00:00.000', 120, 556111, 25  UNION ALL
    SELECT '2018-09-22 00:00:00.000', 129, 346686, 8   UNION ALL
    SELECT '2018-09-22 00:00:00.000', 162, 354247, 86  UNION ALL
    SELECT '2018-09-22 00:00:00.000', 159, 382897, 150 UNION ALL
    SELECT '2018-09-22 00:00:00.000', 120, 556111, 25  UNION ALL
    SELECT '2018-09-23 00:00:00.000', 129, 346686, 23  UNION ALL
    SELECT '2018-09-23 00:00:00.000', 162, 354247, 146 UNION ALL
    SELECT '2018-09-23 00:00:00.000', 159, 382897, 9   UNION ALL
    SELECT '2018-09-23 00:00:00.000', 94,  570135, 23
)

SELECT t1.*
FROM yourTable t1
INNER JOIN
(
    SELECT
        CONVERT(char(10), ROOMDATE, 120) AS ROOMDATE,
        MAX(quantity) AS max_quantity
    FROM yourTable
    GROUP BY CONVERT(char(10), ROOMDATE, 120)
) t2
    ON CONVERT(char(10), t1.ROOMDATE, 120) = t2.ROOMDATE AND
       t1.quantity = t2.max_quantity
ORDER BY
    t1.ROOMDATE;

View schema
Execution time: 0 sec, rows selected: 3, rows affected: 0, absolute service time: 0,16 sec