Question

Four bells are heard at intervals of 2,3,5 and 7 minutes respectively. If all bells toll together exactly at 9 a.M., they will again be heard together at

Answer 1

They will again be heard together at 12 : 30 PM.

Four bells are heard at intervals of 2 , 3 , 5 and 7 minutes respectively. If all bells toll together exactly at 9 : 00 AM.

they will again be heard together at ...

Four bells are heard at intervals of 2 , 3 , 5 and 7 minutes respectively.

so, they will toll together = LCM{2, 3, 5, 7}

• here 2, 3 , 5 and 7 are different prime numbers, so the LCM must be the product of these numbers.

= 2 × 3 × 5 × 7 = 210 min

we know, 1 hr = 60 min

⇒210 min = 180 min + 30 min = 3 × 60 min + 30 min

= 3 hr 30 min

now 9 : 00 AM + 3 hr 30 min = 12 : 30 PM

Therefore they will again be heard together at 12 : 30 PM.

Answer 2

Answer:

At 12.30 PM

Step-by-step explanation:

Given data

four bells are heard at intervals of  2, 3, 5, 7 minutes

all bells toll together exactly at 9 AM  

Here we need to find when will they toll together again

⇒ Find Lcm of 2, 3, 5, and 7

⇒  2 ×3 ×5 ×7 = 210

⇒ for every 120 minutes 4 bells will toll together

⇒ [ 210 minutes = 3 hours 30 minutes ]  

⇒ if all bells are toll together at 9 AM exactly after 3 hours 30 minutes all bells toll together  

⇒ 9 + 3 hours 30 minutes = 12.30 PM  

⇒ at 12.30 PM all bells toll together