A bell rings every 18 minutes. A second bell rings every 24 minutes. A third bell rings every 32 minutes. If all the three bells ring at the same time at 8 o'clock in the morning, at what other time will they all ring together ?

(a) 12 : 40 hrs
(b) 12 : 48 hrs ✓ UPSC's answer
(c) 12 : 56 hrs
(d) 13 : 04 hrs

Why the answer is (b)

• The bells ring together only after a time that is a common multiple of 18, 24, and 32 minutes.

• Factorize: 18 = 2 × 3², 24 = 2³ × 3, and 32 = 2⁵.

• The LCM takes the highest powers: 2⁵ × 3² = 32 × 9 = 288 minutes.

• 288 minutes equals 4 hours 48 minutes.

• Adding 4 hours 48 minutes to 8:00 gives 12:48, so option (b) follows.

Why the other options are wrong

(a) 12 : 40 hrs: 12:40 is 280 minutes after 8:00, and 280 is not a multiple of 18, 24, or 32.
(c) 12 : 56 hrs: 12:56 is 296 minutes after 8:00, and 296 is not a multiple of 18, 24, or 32.
(d) 13 : 04 hrs: 13:04 is 304 minutes after 8:00, and 304 is not a multiple of 18, 24, or 32.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.