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Previous Year Question (PYQs)



A watch ticks 90 times in 95 seconds and another watch ticks 315 times in 323 seconds. If both watches are started together, how many times will they tick together in the first hour?





Solution

Time for one tick of first watch = 95/90 sec = 19/18 sec Time for one tick of second watch = 323/315 sec = 323/315 sec Their tick intervals = 19/18 and 323/315. LCM of time intervals = (19/18, 323/315) → LCM = (GCD of numerators/LCM of denominators) Simplify ratio-based → They tick together every 19 × 323 / LCM(18, 315) seconds ≈ every 19.2 seconds (approx). So, in one hour (3600 seconds): 3600 / 35.6 ≈ 101 times.


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