flash lights

[hemant_rajput]

Q17 . At a bookstore, "MODERN BOOK STORE" is flashed using neon lights. The words are individually flashed at long intervals of 5/2, 17/4 and 41/8 sec resp. , and each word is put off after a second. The least time after which the full name of the bookstore can be read again is?
a. 49.5
b. 73.5
c. 1744.5
d. 855

[vkb001]

Initially, every word is flashed for a second. From then, the interval for which each word is put off differs. So, the time length till the next flash for each of the words is 1+5/2, 1+17/4, 1+41/8 = 3.5, 5.25, 6.125.

We need an integer number of each of these durations so that the cumulative duration of each of these words is equal. To put it simply,

m(3.5) = n(5.25) = k(6.125) where m,n,k are all integers.

We need to find the least common multiple of the three numbers.

LCM(3.5,5.25,6.125) = 73.5.

Another way to figure this out in the exam is to check with each number.

Step 1: Try 49.5 (with the lowest)

49.5/3.5 is not an integer. So, reject this option.

Step 2: Try 73.5

73.5/3.5 = 21 (integer!)
73.5/5.25 = 14 (integer!)
73.5/6.125 = 12 (integer!)

BINGO! Answer's (b)