Rewrite your query this way instead:

select A.year, A.quarter, A.month, B.status,COUNT(distinct B.centre_id) AS c_centre_idFROMAINNER JOIN B ON B.date_id = A.date_id AND B.status = '2'WHEREA.year in ('YR11', 'YR12')GROUP BY A.year, A.quarter, A.month, B.status

It makes is a lot easier to read.

And please provide the output from:

SHOW CREATE TABLE [yourTableNameHere]

and the output from:

EXPLAIN [your query here]

EXPLAIN PLAN

id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE A ALL PRIMARY,year 1037 Using where; Using temporary; Using filesort
1 SIMPLE B ref date_id,status date_id 4 test.A.date_id 1521 Using where

one correction : Its reading approximately 1 Million rows to get 5 rows resultset because of count function and its taking 7 to 8 sec.

Table B
CREATE TABLE `B` (
`paynumber` varchar(20) NOT NULL DEFAULT '',
`date_id` int(11) unsigned NOT NULL,
`Amount` double DEFAULT NULL,
`LoanStartDate` date DEFAULT NULL,
`centre_id` bigint(20) unsigned NOT NULL,
`category_id` bigint(20) DEFAULT NULL,
`Towntype` varchar(40) DEFAULT NULL,
`groupname` char(7) NOT NULL,
`status` tinyint(3) unsigned NOT NULL,
`checks` tinyint(11) DEFAULT NULL,
PRIMARY KEY (`paynumber`,`date_id`),
KEY `paynumber` (`LoanRefNumber`),
KEY `date_id` (`date_id`),
KEY `centre_id` (`centre_id`),
KEY `category_id` (`category_id`),
KEY `status` (`status`),
KEY `groupname` (`groupname`),
KEY `checks` (`checks`)
) ENGINE=MyISAM DEFAULT CHARSET=latin1 ROW_FORMAT=DYNAMIC

Table A

CREATE TABLE `A` (
`date_id` int(10) unsigned NOT NULL DEFAULT '0',
`year` varchar(10) DEFAULT NULL,
`month` int(10) unsigned DEFAULT NULL,
`quarter` int(10) unsigned DEFAULT NULL,
PRIMARY KEY (`date_id`) USING BTREE,
KEY `year` (`year`),
KEY `year` (`month`),
KEY `year` (`quarter`)
) ENGINE=MyISAM DEFAULT CHARSET=latin1 ROW_FORMAT=DYNAMIC