Question

Three bulbs red, green and yellow flash at intervals of 80 seconds, 90 seconds and 110 seconds. All three flash together at 8:00 am. At what time will the three bulbs flash altogether again? *
8​

Answer 1

Answer:

10:12a.m.

Step-by-step explanation:

As already given in the question we need to find a further time when all these bulbs flash again, so we are indicated that we need to find the LCM of 80 , 90, 110 to reach the answer.

Step 1: LCM(80,90,110)  

      80 = 2⁴ X 5

      90 = 2 X 3² X 5

      110 = 2 X 5 X 11

Therefore, LCM = 2⁴ X 3² X 5¹ X11¹

                          = 7920 seconds

Step 2: Convert 7920 seconds to hours

 here you can convert the numbers depending on your convenience either from sec. to min.

7920 seconds = 7920/ 60 mins

                        = 132 minutes

hence this gives 2 hr 12 minutes

STEP 3: Add 2 hours 12 minutes to 8:00 a.m.

hence the answer 10:12a.m.

Answer 2

Three bulbs flash altogether again at 10:12 am

Given :

• Three bulbs red, green and yellow flash at intervals of 80 seconds, 90 seconds and 110 seconds.
• All three flash together at 8:00 am.

To find : The time when the three bulbs flash altogether again

Solution :

Here it is given that three bulbs red, green and yellow flash at intervals of 80 seconds, 90 seconds and 110 seconds

We now find the LCM of 80 , 90 , 110

80 = 2 × 2 × 2 × 2 × 5

90 = 2 × 3 × 3 × 5

110 = 2 × 5 × 11

LCM

= 2 × 2 × 2 × 2 × 3 × 3 × 5 × 11

= 7920

Now 3600 seconds = 1 hour

∴ 7920 seconds

= 2 hour 720 seconds

= 2 hour 12 minutes

Since all three flash together at 8 : 00 am

Hence the time when the three bulbs flash altogether again

= 8 : 00 am + 2 hour 12 minutes

= 10 : 12 am

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