CAT 2002 QA Question 47 · Algebra - Number Theory

The words MODERN, BOOK and STORES appear after 5/2, 17/4 and 41/8 seconds respectively and are put off after 1 second.

So, if all the words flashed together at t = 0 seconds, then

MODERN will flash after (5/2 + 1) = 7/2 seconds

BOOK will flash after (17/4 + 1) = 21/4 seconds

STORES will flash after (41/8 + 1) = 49/8 seconds.

So, all the words will flash together again after LCM(7/2, 21/4, 49/8) seconds.

∴ L.C.M. $\left(\frac{7}{2},\frac{21}{4},\frac{49}{8}\right)=\frac{\mathrm{L}.\mathrm{C}.\mathrm{M}. \mathrm{of} \mathrm{Numerators}}{\mathrm{H}.\mathrm{C}.\mathrm{F}. \mathrm{of} \mathrm{Denominators}}=\frac{147}{2}=$ 73.5 seconds

Hence, option (a).