At a bookstore, ‘MODERN BOOK STORE’ is flashed using neon lights. The words are individually flashed at the intervals of 2.5 s, 4.25 s and 5.125 s respectively, and each word is put off after a second. The least time after which the full name of the bookstore can be read again for a full second is

In this problem, the lights are flashed at the intervals 2.5, 4.25 and 5.125 seconds and put off after one second each.

The total duration of intervals of these lights are (2.5+1) = 3.5 s, (4.25+1) = 5.25 s and (5.125+1) = 6.125 s.

We have to find the minimum duration. It would be the LCM of thes three numbers.
Since each word is put after a second. So LCM [$$(\frac{5}{2}+1 )(\frac{17}{4}+1)(\frac{41}{8}+1)$$] = LCM of numerator / HCF of denominator = 49*3/2 = 73.5. Hence they will glow for full one second after 73.5-1 =72.5 sec.