Question

The signboard outside the department store
Ram and Shyam' lights up as described below
When the switch is turned on all the three words
light up and remain lighted for 3 seconds. After that
the first word is switched off for 47/6 seconds, the
second word is switched off for 4/3 seconds and the
third word is switched off for 17/3 seconds. Then
each word is again switched on for 3 seconds and
then switched off for the time duration mentioned.
This process continues repeatedly. After how many
seconds of switching on the signboard will the entire
board be switched on for the second time for 3 seconds?
(A) 121/3 (B) 125/3 (C) 128/3
(D) 130/3

Answer 1

Given :  The signboard outside the department store  Ram and Shyam' lights up  Each word for 3 secs and then switch off for few second

To find : After how many  seconds of switching on the signboard will the entire  board be switched on for the second time for 3 seconds

Solution:

'

Each word  lit for 3 secs first

Then  1st word is switched off for  47/6 secs  

Second word  switched off for 4/3 secs = 8/6 sec

& third word switched off for  17/3 Sec  = 34/6 sec

LCM of ( 47/6 + 3) , ( 8/6 + 3)  , ( 34/6 + 3)

= (65/6) , (26/6) , (52/6)

65 = 13 * 5

26 = 13 * 2

52 = 13 * 2 * 2

LCM = ( 2  * 2 * 5 * 13 /6)  = 260/6

= 130/3

After 130/3 Secs of switching on the signboard the entire  

board will  be switched on for the second time for 3 seconds

option D is correct'

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