Question

The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7a.m.,at what time will they change simultaneously again?​

Answer 1

ᴛʜᴇ ᴛʀᴀғғɪᴄ ʟɪɢʜᴛ ᴀᴛ ᴛʜʀᴇᴇ ᴅɪғғᴇʀᴇɴᴛ ʀᴏᴀᴅ ᴄʀᴏssɪɴɢ ᴄʜᴀɴɢᴇ ᴀғᴛᴇʀ ᴇᴠᴇʀʏ 48 sᴇᴄᴏɴᴅs,72 sᴇᴄᴏɴᴅs ᴀɴᴅ 108 sᴇᴄᴏɴᴅs ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ.

sᴏ ʟᴇᴛ ᴜs ᴛᴀᴋᴇ ᴛʜᴇ ʟᴄᴍ ᴏғ ᴛʜᴇ ɢɪᴠᴇɴ ᴛɪᴍᴇ ᴛʜᴀᴛ ɪs 48 sᴇᴄᴏɴᴅs, 72 sᴇᴄᴏɴᴅs, 108 sᴇᴄᴏɴᴅs

⇒ 48 = 2 × 2 × 2 × 2 × 3

⇒ 72 = 2 × 2 × 2 × 3 × 3

⇒ 108 = 2 × 2 × 3 × 3 × 3

ʜᴇɴᴄᴇ ʟᴄᴍ ᴏғ 48, 72 ᴀɴᴅ 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)

ʟᴄᴍ ᴏғ 48, 72 ᴀɴᴅ 108 = 432

sᴏ ᴀғᴛᴇʀ 432 sᴇᴄᴏɴᴅs ᴛʜᴇʏ ᴡɪʟʟ ᴄʜᴀɴɢᴇ sɪᴍᴜʟᴛᴀɴᴇᴏᴜsʟʏ

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ

60 sᴇᴄᴏɴᴅs = 1 ᴍɪɴᴜᴛᴇ

sᴏ ᴏɴ ᴅɪᴠɪᴅɪɴɢ 432 / 60 ᴡᴇ ɢᴇᴛ 7 ᴀs ϙᴜᴏᴛɪᴇɴᴛ ᴀɴᴅ 12 ᴀs ʀᴇᴍɪɴᴅᴇʀ

ʜᴇɴᴄᴇ, 432 sᴇᴄᴏɴᴅs = 7 ᴍɪɴ 12 sᴇᴄᴏɴᴅs

∴ ᴛʜᴇ ᴛɪᴍᴇ = 7 ᴀ.ᴍ. + 7 ᴍɪɴᴜᴛᴇs 12 sᴇᴄᴏɴᴅs

ʜᴇɴᴄᴇ ᴛʜᴇ ʟɪɢʜᴛs ᴄʜᴀɴɢᴇ sɪᴍᴜʟᴛᴀɴᴇᴏᴜsʟʏ ᴀᴛ 7:07:12 ᴀ.ᴍ

Answer 2

Step-by-step explanation:

LCM of 48 seconds, 72 seconds and 108 seconds.

48 = 2×2×2×2×3

72 = 2×2×2×3×3

108 = 2×2×3×3×3

LCM= 2×2×2×2×3×3×3

= 432

Now,

So, divide 432 by 60...

We will get 7.2 seconds..

Now,

1 minute = 60 seconds

So, 7 minutes = 7×60 seconds= 420 seconds.

Now, Subtract 432 and 420...

= 4 3 2

- 4 2 0

0 1 2

☆Hence, 432= 7 minutes 12 seconds...

So, at 7 minutes 12 seconds past 7 a.m., they will change simultaneously again...