The traffic lights at 3 different road crossings change after every 48 sec 72 sec and 108 sec respec...........

Quantitative Aptitude (MTS) LCM, HCF

The traffic lights at 3 different road crossings change after every 48 sec, 72 sec and 108 sec, respectively. If they all change

simultaneously at 8:20 a.m., then at what time will they next change again simultaneously?

This questions was previously asked in

SSC MTS 7th July 2022 Shift-1

8:27:12 a.m.

8:33:32 a.m.

9:12:18 a.m.

8:40:14 a.m.

Here’s how you figure this out:

- The lights change every 48 sec, 72 sec, and 108 sec. To find when they line up again, you need the Least Common Multiple (LCM) of these numbers.

- Let’s break that down:

- 48 = 2×2×2×2×3

- 72 = 2×2×2×3×3

- 108 = 2×2×3×3×3

- The LCM is 2^4 × 3^3 = 16×27 = 432 seconds.

- 432 seconds is 7 minutes and 12 seconds.

- They all changed together at 8:20 a.m. Add 7 minutes 12 seconds: that’s 8:27:12 a.m.

Let’s check your options:

- Option 1: 8:27:12 a.m. — This matches our math.

- Option 2: 8:33:32 a.m. — That’s 13:32 minutes later, not correct.

- Option 3: 9:12:18 a.m. — Over 52 minutes later, not correct.

- Option 4: 8:40:14 a.m. — Over 20 minutes later, not correct.

So yes, the right answer is Option 1: 8:27:12 a.m.

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