# Difficult Number System Solved QuestionAptitude Discussion

 Q. The three words "TATA Assets Rock" are flashed such that the words individually are switched on at regular intervals of 4,7 and 9 seconds respectively and after they are switched on, the words are switched off after 2 sec, 4 sec and 5 sec respectively. If at time '$t$' all the words happened to switch off simultaneously, find the least time '$t$' which all three words will switch on simultaneously.
 ✖ A. 252 sec ✖ B. 126 sec ✔ C. 94 sec ✖ D. 38 sec

Solution:
Option(C) is correct

The first word will switch on after $4x+ (4-2)$ seconds from $t$

The second word will switch on after $7y+ (7-4)$ seconds from $t$

The third word will switch on after $9z+ (9-5)$ seconds from $t$.
⇒ If at $t'$, all the switches on together
$t' - t = 4x+2 = 7y+5 = 9z+4$

We want the least value of $t'-t$ for which $x, y$ and $z$ are integers.

Check the options we get 94 the least option.

## (2) Comment(s)

Rajesh
()

second word is switched on after 7 seconds and stays in on condition for 4 sec ,so after every 11(7+4) sec word will be just sitched off or will switch on after 7 sec..that means 94/11 remainder is 6 then from these 6 seconds world will be on for first 4 sec and den after 7 sec again will be on..but remaing sec from 6 is just 2 so how is it possible?

Saikiran
()

Yes I had this doubt too. But since we are not sure, if all had started exactly from same tym..

We can assume the leas tym when the values appear next to each other, there is chance they will be on simultaneously..

So acc to condns, TATA appears after 94secs, Assests appear after 95secs, Rock appear after 93secs..

First instance of all three coming next to next, so in given options 94 is available..

Can take this as solution.

(This is just an imaginative concept, if people tend to try something. )